OUTLINES OF THE
EVOLUTION OF WEIGHTS AND MEASUEES
AND THE METRIC SYSTEM
OUTLINES OF
THE EVOLUTION OF
WEIGHTS AND MEASURES
AND
THE METRIC SYSTEM
BY
WILLIAM HALLOCK Ph.D.
PROFESSOR OF PHYSIOS IN COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK
AND
HERBERT T. WADE
EDITOR FOR PHYSICS AND APPLIED SCIENCE, ' THK NEW INTERNATIONAL ENCYCLOPAEDIA
THE MACMILLAN COMPANY
LONDON : MACMILLAN AND CO. LTD.
1906
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GLASGOW I PRINTED AT THE UNIVERSITY
BY ROBERT MACLEHOSE AND CO. LTD.
PREFACE.
In the following pages it has been the aim of the authors to
present in simple and non-technical language, so far as possible, a
comprehensive view of the evolution of the science of metrology
as it is now understood. Inasmuch as the introduction of the
Metric System into the United States and Great Britain is a
topic of more or less general interest at the present time, it has
seemed that a work designed both for the student of science and
for the general reader, in which this system is discussed in its
relation to other systems of weights and measures past and
present, would fill a certain need. While there are many works
on metrology that treat at considerable length the historic and
scientific sides of the subject, as well as the economic and
archaeological questions involved, and a large number of books
and pamphlets dealing with the teaching of the Metric System,
besides those supplying tables and formulas for converting from
one system to the other, yet there is apparently a distinct lack of
works, which in small compass discuss the subject comprehensively
from its many points of view. Indeed, the student of metrology
is apt to be embarrassed by an extensive literature rather than
by any deficiency in the amount of collected material, though
much of the latter, to be sure, is included in various Eeports and
Proceedings of learned societies and official documents rather than
in single works. A large amount of this literature devoted to
metrology represents a minute specialization and critical analysis
often discussing either a certain epoch, or a single system or
group of weights and measures, where the treatment is from the
standpoint of either archaeology, economics, or physical or mathe-
matical science, and but rarely combining the three points of
vi PREFACE
view. In addition, much of this literature is of an argumentative
nature, and debate and discussion rather than definite conclusions
compelling universal acceptance seem to be characteristic of
metrological writing.
It has been the intention of the authors to consider briefly and
systematically the general history of weights and measures, the
scientific methods by which units and standards have been
determined, the concrete standards by which the units are
represented, and the present aspect of modern systems of weights
' and measures, together with the difficulties and advantages
involved in any proposed changes. Experience derived while
giving instruction in physics to students in applied science has
suggested the general plan of treatment, and it has seemed
desirable to present from an American standpoint the most
essential facts in as logical relation as is possible in a science
that is often marked by conditions quite illogical. From the
copious notes and bibliographical references, which it is hoped will
be appreciated by advanced students and those specially interested
in the subject, it will be seen that at the outset any claims to
striking originality must be dismissed, and the obligations of the
authors to the various authorities mentioned in the notes are
ungrudgingly acknowledged.
The authors hope that their work will serve two useful ends :
first, as an introduction to metrological science designed especially
for the student entering on the study of physics to whom a
knowledge of units and standards is most necessary ; and second,
as preparatory to an intelligent understanding of the discussions
involved in the proposed adoption of the Metric System by
English-speaking peoples, especially by those to whom Metric
and Anti-Metric arguments are being addressed with such
frequency and persistence. It has been the intention of the
authors to avoid as far as possible all controversy for several
reasons ; the first and most important of which is that this side
of the question has been and is being abundantly covered
elsewhere, so that it has seemed preferable in this work to
include a mere statement of facts rather than to repeat or even
add to the arguments. Such has been their intention, but they
are also compelled to admit that they are supporters of the
Metric propaganda, and they must ask indulgence for any
PREFACE vii
departures from the plan determined on. However that may
be, they have endeavored to give a fair and concise history of
the Metric System so that its logical development and character-
istics will be apparent, and this, together with the experience of
European nations as briefly described, will supply sufficient data
on which may be formed an intelligent opinion as to the
desirability of adopting in America and Great Britain at an
early date the International System of weights and measures.
In view of the fact that such a work has involved the use of a
vast number of authorities, it is manifestly impossible to specify
in detail other than in the notes the great indebtedness on the
part of the authors to the labors of many famous metrologists.
Naturally they have consulted freely the classic work of Mechain
and Delambre, Base du sysUme Mttrique ; General Morin's
Notice historique sur le systtme Mdtrique ; Bigourdan's Le syst&me
MStrique ; Guillaume's La Convention du Metre ; and his excellent
little treatise on UniUs et Etalons, as well as Benoit's Eeport on
Standards of Length to the International Physical Congress of
1903. In addition they have used the various publications of the
International Bureau of Weights and Measures. For ancient
weights and measures many sources have been consulted, while
for English standards and metrology the works of Chisholm and
Chaney have been found most helpful, but they have been
supplemented by various papers of Parliamentary commissions
and the Proceedings of scientific societies. In the United States
the Keports and other papers of the Coast and Geodetic Survey,
the recently established National Bureau of Standards, and the
Committees on Coinage, Weights and Measures, of the House of
Eepresentatives have formed a nucleus that has been supple-
mented by extensive reference to other scientific literature.
In conclusion the authors would gratefully acknowledge their
obligations to M. Ch. Ed. Guillaume, Assistant Director of the
International Bureau of Weights and Measures, and Professor
S. W. Stratton, Director of the U.S. Bureau of Standards, who
most kindly consented to look over the proofs and have
rendered assistance in many substantial ways.
CONTENTS.
CHAPTER I.
PAGE
Beginnings and Development of the Science of Metrology, 1
Underlying Principles of Metrology. Development of the Science
among Primitive Peoples. Metrology of the Babylonians. Hebrew
Metrology. Weights and Measures among the Egyptians. Greek
Weights and Measures. The Roman System and its Spread.
Mediaeval Conditions. Development of Anglo-Saxon Metrology.
Early French Weights and Measures. European Conditions
Generally.
CHAPTER II.
Origin and Development of the Metric System, - - 41
Reasons for the Change and Preliminary Efforts. Scientific and
Other Steps in its Development. The Derivation of the Meter
and Kilogram. Adoption of the System. Method of bringing
about the Change. Systeme Usuelle. Spread of the Metric
System and Compulsory Legislation of 1837. The Metric Treaty
and the Formation of the International Bureau of Weights and
Measures. Work and Organization of the Bureau.
CHAPTER III.
Extension of the Metric System throughout Europe and
elsewhere, - 80
Confusion Existing and Reasons for the Change. Dates and
Methods of Making the Change — Germany. Austria. Hungary.
Belgium. Egypt. Greece. Italy. Japan. Netherlands. Portugal.
Russia. Spain. Sweden and Norway. Switzerland. Turkey.
Great Britain. Mexico. South and Central America. Table
showing Dates when Metric System was adopted.
PAGE
x CONTENTS
CHAPTER IV.
Weights and Measures in the United States, - 109
Connection of Weights and Measures with Systems of Currency.
Development of the Decimal Principle. Early National Legisla-
tion. Various Plans Proposed. John Quincy Adams' Report on
Weights and Measures. The Development of a National System
and Progress towards Uniformity. Early Standards and Definitions.
Spread of the Metric System. Summary of Metric Legislation.
CHAPTER V.
The Metric System of To-Day — Its Essential Character-
istics and Fundamental Principles, - - - - 135
General Characteristics. Linear Measures. Superficial Measures.
Cubical Measures. Measures of Capacity. Measures of Mass.
CHAPTER VI.
The Metric System for Commerce, - - - - - 150
The Advantages of a Universal System. The Metric System for
International Trade. Its Applicability to the Ordinary Transaction
of Commerce. The Advantages of a Homogeneous and Decimal
System.
CHAPTER VII.
The Metric System in Manufacturing and Engineering, 172
Simplicity of Metric System. Ease with which Change could be
made. Question of Gauges. Linear Measurements in Mechanical
Engineering. The Question of Screw Threads. Introducing the
Metric System into a Machine Shop.
CHAPTER VIII.
The Metric System in Medicine and Pharmacy, - - 191
General Nature of its Use and its Advantages. Adoption by
U.S. Army and Navy Medical Departments.
CONTENTS xi
CHAPTER IX.
PAGE
International Electrical Units, - - - 199
The Absolute System. Derivation of Electrical Units from the
Metric System. The C.G.S. System of the British Association.
Definitions of Electrical Units at Chicago, 1893. Specifications
for the Practical Application of these Definitions. New Magnetic
Units. Shortcomings of Present Units.
CHAPTER X.
Standards and Comparison, - - - - - - 218
Nature and History of Standards. Methods of Comparison.
Present Day Standards. Definition of the Meter in terms of the
Wave Length of Light.
APPENDIX.
Tables of Equivalents and Useful Constants, - - 267
U.S. Legal Equivalents. British Legal Equivalents. Table for
Conversion of Units of Length. Table for Conversion of Units
of Mass. Equivalents, Millimeters and Fractions of an Inch.
Comparison of Prices : Length — Inches and Centimeters, Feet and
Meters, Yards and Meters, Miles and Kilometers. Areas — Acres
and Hectares. Capacity — Liquid Quarts and Liters, Gallons and
Liters. Mass — Avoirdupois Pounds to Kilograms, Comparison of
Tons and Pounds. Capacity — Various Equivalents. Mass — Various
Equivalents. Apothecaries' Weight — Table of Equivalents. Den-
sity, Melting Point and Boiling Point Tables. Thermometer Scales
— Table of Equivalents. Miscellaneous Constants and Equivalents.
Index, - - 295
CHAPTEE I.
ORIGIN AND DEVELOPMENT OF THE SCIENCE OF
METROLOGY.
Few questions concern the human race more directly and
universally than the subject of weights and measures. In fact,
so intimate is this connection that the common weights and
measures of a people bear much the same relation to it as does
the language of ordinary speech, being assumed and applied in
their daily occupations without active thought, and resisting
changes and reforms, even when brought about by the most
strenuous efforts and with convincing proof of their desirability
or necessity. For the origin of weights and measures it is
necessary to go back to the earliest days of the human race and
deal with the elementary mental processes of primitive man. The
idea of measuring must have been closely akin to that of
number, which, of course, implied the perception that certain
objects could be grouped together either actually or at least
ideally. The next step would be the comparison of the various
objects of such a group, and this would involve a simple ratio
in terms of one of the members of the group. When the
comparison was extended to other groups, there was need of a
standard, and, when various classes of objects were compared,
a standard had to be selected which would answer in common.
Such standards would readily suggest themselves. If it took a
certain number of days and nights to make a journey, the distance
travelled in one day, that is from one sunrise or sunset to
the next, would straightway be considered as a natural measure
of journeys of considerable duration, while, for shorter distances,
A
2 EVOLUTION OF WEIGHTS AND MEASURES
the pace as a regularly recurring interval would be adopted
for measuring the total distance, and the single pace would
be taken as a unit.
For measuring still smaller distances the primitive man would
take, say the length of his foot or the breadth of his hand, as it
would be most convenient for him to employ as units in his
measurements the objects usually at hand, and it was but
natural that the dimensions of the body would furnish such
units. Thus for linear measures there would be employed the
breadth of the first joint of the forefinger, the breadth of the
hand, the span of the extended fingers of one hand, the length of
the foot, the length of the forearm, the step or single pace, the
double pace, and the distance between the tips of the fingers
when the arms were outstretched. All of these distances figured
in the early systems of linear measures of the ancients, and, in
fact, great diversity of measures was a characteristic of early
civilization, due to the fact that originally only the convenience
of the individual had to be consulted. With the growth of
society the tendency was toward uniformity, and this tendency,
with but occasional retrogressions, has been maintained. When
several persons were concerned in the comparison of the size of
an object or some other kind of measurement, it was necessary
to consult the convenience of the group rather than that of the
individual, while with the development of trade there was
also added the idea of equity.
Along with the general tendency of progress from diversity
to uniformity of measures in the evolution of society, must also
be considered the securing of uniformity of single measures.
Thus, if a pace or length of a forearm was a convenient unit for
a number of individuals, it would soon become necessary to
specify the class of individuals, or, better still, the single indi-
vidual whose pace or forearm was to be the standard; was it to
be that of a man six feet in height or one considerably shorter ?
Such a discussion could not but lead to the actual measuring
of the pace or forearm which would by common consent serve as
the measure, and then by laying off the distance on some surface
a standard or concrete reproduction of the unit would be con-
structed which would answer for the family or small group*
Just as it was necessary for the family to come to some
THE SCIENCE OF METROLOGY 3
understanding as to what measures would be standard for their
household, so it was soon realized that the interests of all
would best be subserved if a single system should be employed
throughout the tribe, either by a gradual adoption of a common
mean, or by having some standard imposed by authority emana-
ting from the ruler or headmen of the tribe. This latter practice
was the more prevalent, and, remarkable to say, has persisted
to modern times. So late as the time of Henry I. the length of
the English yard, according to tradition, was fixed by the length
of the sovereign's arm, while even in the United States in nearly
all cases the national standards of weights and measures have
been determined by executive order rather than by legislative
action.
While the foregoing observations would also hold true in the
case of weights, yet in connection with the latter there are
certain additional matters to be considered. When the primitive
man had advanced in civilization to a point where he looked
beyond his immediate needs, he would doubtless own a certain
number of slaves and domestic cattle, and his life being spent in
an habitation or home more or less permanent, it would be
natural for him to accumulate stores of grain and other
substances both for his future wants and to barter for other
commodities. Now, it seems that the earliest unit of wealth
and basis of exchange was the ox or cow, and this soon found
an equivalent in a certain amount of gold, a substance which,
on account of its practically universal distribution and its
uniform scarcity, could readily be given a fixed value in terms
of cows or oxen.1 This would involve some rude form of
measurement, such as a goose-quill for the measurement of gold
dust by capacity, or a linear measurement if the gold was in the
form of wire or strips, and eventually the use of a primitive
balance with the natural seeds of plants for weights. These
seeds indisputably were the first weights, as can be proved by
studying the habits of primitive peoples past and present, where
such use of seeds has been and is practically universal, and this
custom, furthermore, has survived in the grains of the Anglo-
Saxon weights and the carat (from the Arab carob or bean) of
the dealers in precious stones. But this early weighing was
1Ridgeway, Origin of Metallic Money and Weights (Cambridge, Eng., 1892).
4 EVOLUTION OF WEIGHTS AND MEASURES
confined to gold for purposes of trade, and to other metals, such
as silver and copper, when they were subsequently used for
a similar purpose; and this is amply demonstrated by early
Egyptian records where mention is made of weighing only gold,
silver, and copper, and lapis lazuli, until the time of the seven-
teenth dynasty. As it was not until the seventh century B.C.
that coined money was used, this weighing of metals was
universal, and the use of the balance was required in practically
all transactions, as when " Abraham weighed to Ephron the
silver which he had named in the audience of the sons of
Heth, four hundred shekels of silver, current money with the
merchant " (Gen. xxiii. 16).
It followed naturally from such universal weighing that
certain units should be formed, made up of a certain number of
seeds and reproduced by stone or metal standards. Though we
may agree with Eidgeway that the , earliest weighings were
empirical, and were carried on by seeds and natural standards
" before ever the sages of Thebes or Chaldaea had dreamed of
applying to metrology the results of their first gropings in
Geometry or Astronomy," 1 yet we must admit that some sort of
a mathematical system of units of weight was bound to come
where weighing was so widespread. Then with the development
of civilization, especially as regards science and commerce, it was
but natural that these weights should be defined either by royal
decree or by common consent, and be based upon a standard
which, according to some metrologists, was scientifically deter-
mined, or in the opinion of others was merely an arbitrary
weight or weights. At all events it must be borne in mind in
considering questions of metrology from the earliest times down
to within the last two centuries that accuracy in weights and
measures was neither demanded nor possible, and that attempts
of archaeologists accurately to weigh the weights or measure the
linear scales from old ruins, and to use small differences in
forming their theories, are in most cases quite unwarranted.
There is, however, indisputably a certain amount of corre-
spondence among the weights and measures of antiquity due to
commercial intercourse which took place both by sea and by
caravan, and which was much greater than we would be apt to
1 Ridgeway, p. 232.
THE SCIENCE OF METROLOGY 5
suspect, and this should of course receive due weight in all
discussions of the metrology of the ancients.
For the measure of capacity it— is— tfuito obvious tha-t the
earliest units were natural objects such as eggs or gourds, and that a
basket or jar would be constructed by a certain tribe which would
be of a convenient capacity for the purposes for which it was
used, such as carrying grain or water. Such natural or arbitrary
units would straightway find application and would doubtless fill
all needs, as capacity measurements would be of the simplest
nature possible. In—kcct, with certain primitive - peoples, as is
now the case among some Asiatic tribes, units of measure of
capacity were quite unknown, and it is the general tendency for
units of capacity to come after units of weight. If we are to
follow the theories of some metrologists we must assume that the
ancients derived their units of capacity from a cube one of whose
sides was the linear unit, and that the unit of weight was this,
or a proportionate cube, which was filled with pure water. In
fact, such a process would give a unit of area by taking a square
whose side was a linear unit, and a cubical measure formed by a
unit cube whose edge was a linear unitj Whether or not the
ancients followed such a process of reasoning it is impossible to
say, but on both sides of the question there are many arguments
which will briefly be referred to a few pages further on.
While the development of weights and measures is a gradual
evolution, yet it is a complex matter to which so many influences
have contributed that it is difficult to trace any clear course or
logical development. Ethnic conditions, the whims and caprices
of rulers, imposition and fraud, conquest, and methods and habits
of thought and life, all in turn have had their effect. Never-
theless the growth of scientific knowledge and its application, the
influence of the market-place, as well as that of a broader
commerce and laws and customs, in every nation have tended to
bring together into something more or less resembling a system
all matters connected with weighing and measuring built up on
such units as the tribe or nation had selected for their inter-
change of commodities and ideas.
For the units or bases of such systems it is possible to select
two different classes of quantities, arbitrary and natural, and to
use them in their development. By an arbitrary quantity is
6 EVOLUTION OF WEIGHTS AND MEASURES
meant one that is selected without reference to its occurrence in
any natural object or condition, but merely a certain distance,
mass, etc., which will furnish a convenient basis both in its
original state and by its multiples and submultiples, for the
measurements to which it will be applied. In actual practice
the result has been, in spite of many attempts to construct
systems based on natural units, that the fundamental units are
arbitrary, and where interrelated are based upon actual standards
of length rather than distances found in nature. As examples of
natural units might be cited the measures derived from the
human body already mentioned, which readily connect themselves
one with another by certain relations. Thus :
The Digit, ----- equals 1 part
Palm or handbreadth,
„ 4 ,
Span, -----
„ 12 ,
Foot, -
n 16 ,
Cubit,
„ 24 ,
Step or single pace, - - -
„ 40 ,
Double pace, - - - -
„ 80 ,
Fathom, or distance between ex-
tended arms, - - -
n 96 ,
This ratio we find observed in early systems of measurement, and
it must be borne in mind in considering them.
As typical of early natural measures as found in the Orient,
the following passage from the writings of Hiuen Tsiang (Yuan
Chwang), 603-668 A.D., a Chinese traveller and author, of Ho-ran,
written in a.d. 629 in regard to the measures of India, may be
cited : 1
" In point of measurements, there is first of all the yojana
(yu-shen-na) ; this from the time of the holy kings of old has
been regarded as a day's march for an army. The old accounts
say it is equal to 40 li ; according to the common reckoning in
India it is 30 li, but in the sacred book (of Buddha) the yojana
is only 16 li. In the subdivision of distances a yojana is equal
to eight kros'as (keu-lu-she) : a kros'a is divided into 500 bows
(dhanus) : a bow is divided into four cubits (hastas) : a cubit is
divided into 24 fingers (angulis): a finger is divided into 7 barley-
1Beal, Buddhist Records of the Western World (London, 1884), vol. i. p. 70.
THE SCIENCE OF METROLOGY 7
corns (yavas) : and so on to a louse (yuka), a nit (liksha), a dust
grain, a cow's hair, a sheep's hair, a hare's down, a copper water,1
and so on for seven divisions, till we come to a small grain of
dust : this is divided sevenfold till we come to an excessively
small grain of dust (ami) : this cannot be divided further without
arriving at nothingness, and so it is called the infinitely small
(paramanu)."
Leaving out of consideration the source or antiquity of these
particular measures, they may be considered as exemplifying the
use of natural circumstances or objects as units and their connec-
tion into a system. However, as is mentioned in the case of the
yojana, and the same may be found in numerous other instances
in early measures not only in the Orient but throughout the
civilized world, the ancient systems may have contained units
varying in value and in their relation to other units. It may be
said in passing that it is fair to assume that these particular
measures were much older than would at first glance appear from
the date of the work quoted, as India and the adjoining countries
boasted a civilization that was nothing if not conservative, and
traced its traditions to a remote past.
Another example of a natural unit, according to some of the
older authorities on metrology, including Paucton,2 though the
theory is now regarded as entirely erroneous, was the base of the
Great Pyramid, which was constructed equal to the five hundredth
part of a " degree," and was divided into 600 Ptolemaic feet or
400 Ptolemaic cubits. Likewise in the determination of the meter
an attempt was made to measure the ten-millionth part of a
quadrant of a great circle of the earth, but it was subsequently
found that the meter thus obtained did not represent this fraction
with sufficient accuracy, and it was concluded to retain such a meter
as an arbitrary standard and as the basis of the metric system
rather than attempt to secure a new natural unit which might
require subsequent changing with future scientific developments.
Even after the metric system had been developed, Sir John
Herschel, the British astronomer, proposed as a standard the
1 Possibly the size of the small hole in the tamri or copper cup for the admis-
sion of water.
2 Paucton, M&rologie, ou Traits des Mesures, Poids et Monnoies (Paris, 1780),
chap. i. p. 109 et seq.
8 EVOLUTION OF WEIGHTS AND MEASURES
length of the polar axis of the earth, as ,nnAnftnn Part °f
this quantity would give the present British inch very closely.1
Another class of natural units that were employed as the basis
of systems of weights and measures consisted of the dimensions or
weight of grains of barley or corn, a number of such grains being
placed in a row to form such a unit as the English inch, or col-
lected to a certain number to form by their weight an English
pound.
Whether the units be natural or arbitrary there must be some
that are fundamental, and on them can be based and developed
others as civilization, commerce, and science need additional units
to express the magnitudes with which they are forced to deal.
For example, in the eighteenth century it was not possible to
make any measurements of electricity, nor indeed were such
demanded, yet one hundred years later a complete system of
electrical measurements was developed based on measures and
units previously used.2
For fundamental units it is possible and most convenient to
start with the unit of length and develop from it units of weight
and capacity by taking a volume equal to that of a cube, each
side of which is equal to the selected unit of length, and then
filling it with water, as was done with the modern metric system,
and is a feature claimed for the weights and measures of the
ancient Babylonians. Similarly, units of area could be developed
by taking a square whose side is the linear unit, and with the
addition of a unit of time, units of velocity, acceleration, etc.,
could readily be derived. By the time that these and other
required units were obtained, they naturally would become asso-
ciated into a system of more or less logical relation and arrange-
ment. In such a system there necessarily would be a number of
different units for different classes of quantities, and these would
be multiples and sub-multiples of each other. Such arrangements
and systems would reflect the methods of thought of the people
by whom they were developed. Accordingly in ancient Egypt
and also in China we find a decimal system employed as in their
system of numerical notation, while among the Babylonians,
Chaldaeans, Assyrians, and the Egyptians of certain later dynasties
1See chapter vi., p. 164.
2 See chapter ix. — Electrical Units.
THE SCIENCE OF METROLOGY 9-
the basis of division was sexagesimal, as is retained in our modern
notation of time. The Eomans used the duodecimal system,
where the foot, sextarius (measure of capacity), libra (pound), etc.,.
were divided into twelve equal parts. With the Hindus there
was the binary subdivision which was also followed by the Ger-
manic and Teutonic peoples, and also by the Arabs, despite their
decimal system of notation. These examples show how national
or racial conditions affect the development of a system of weights
and measures, and of course as the political, commercial, or intel-
lectual influence of a nation extended it was but natural that
with it would go its weights and measures, which, if not sup-
planting those of other countries, at least in many cases would
have a corrupting and disintegrating influence.
In any attempt at a brief historical survey of the origin and
history of weights and measures there are many matters to be taken
into consideration which prevent a complete and comprehensive
sketch of the subject. For over two centuries there has been much
attention devoted to ancient metrology, and many and contra-
dictory theories have been advanced. They are for the most
part founded on data or hypotheses by no means satisfactory ;
though in nearly all instances plausible cases which often show
the greatest study and ingenuity have been made out by workers
whose sincerity and industry cannot be questioned. In certain
of these systems and theories the ancients are credited with a
knowledge of mathematics, both theoretical and applied, which
some scholars do not think at all warranted, while other systems
have been built up on limited data, often text allusions in ancient
literature and inscriptions, which though harmonious to a greater
or less extent do not absolutely convince one that the harmony is
not quite as much the result of chance as of design.
Assuming that the parts of the body were employed by many
ancient races as the basis of measures of length, it is desirable to
ascertain how these were united into a system and how such a
system spread. It is usual to credit the origin of systems of
weights and measures to Babylon or Egypt, the systems of both
countries showing a common source, and there being various
remains, literary and archaeological, on which have been based
explanations of the origin of all ancient measures. Thus the
great pyramid of Ghizeh, dating from about 4000 B.C., by some has
10 EVOLUTION OF WEIGHTS AND MEASURES
been thought to have an important bearing on metrology, and has
figured in many discussions and theories, since by its dimensions
and inscriptions it supplies data which are susceptible of various
interpretations. Thus Paucton and Jomard,1 two distinguished
metrologists of the eighteenth century, assumed that the side of the
pyramid represented a fraction of a degree of the earth just as
the French scientists based the meter on a fraction of the earth's
quadrant ; while later Prof. Piazzi Smyth2 and Lieut. C. A. L.
Totten3 derived the Anglo-Saxon weights and measures directly
from its dimensions. These theories, as well as the idea that the
great pyramids played an important part in ancient astronomy,
have been amply controverted, and according to the opinion of
Lieut.-Gen. Sir Chas. Warren4 in the light of the most recent
investigations, " The Pyramid is simply a record of the measures,
linear, capacity, and weight, which were in use in former days."
There is nothing astronomical about it except its orientation and
the direction of its great gallery to a point in the northern sky.
There were, however, other great structures in Egypt and
Babylonia in which stone and brick5 of regular dimensions were
used, and even in the earliest times of which we have record it
seems conclusive that there must have existed fairly complete
systems of weights and measures.
According to the Jewish tradition given in Josephus, we are
informed in the quaint language of Dr. Arbuthnot, " that Cain
was the first monied man, that he taught his band luxury and
rapine, and broke the public tranquillity by introducing the use of
weights and measures."6 What happened in the land of Nod,
1 Paucton, Metrologie, ou Traits des Mesures, Poids et Monnoies (Paris, 1780);
■Jomard, Memoire sur le Systeme Me'trique des Anciens Egyptiens (Paris, 1817).
2C. Piazzi Smyth, Life and Work at the great Pyramid (Edinburgh, 1867) ; Our
Inheritance in the great Pyramid (London, 1864). These works and Professor
Smyth's theories are discussed by Dr. F. A. P. Barnard in Proceedings Am.
Metrological Society (New York), vol. iv., 1884, pp. 197-219.
3 Charles A. L. Totten, An Important Question in Metrology (New York, 1884).
4 Warren, "The Ancient Standards of Measure in the East," p. 222, Palestine
Exploration Fund Quarterly, 1899.
5 In Babylonia square bricks were used which measure 13 inches on each edge,
•or \ of the double cubit as given by the Gudea Scale (see p. 14).
6 Arbuthnot, p. 1, Tables of Ancient Coins (London, 1754).
THE SCIENCE OF METROLOGY 11
whither Cain had wandered with his band and where he founded
his city (Genesis iv. 16 and 17), soon must have become universal,
for we find the dimensions of the ark as Noah was told to construct
it given in cubits (Genesis vi. 15).
Apart from such traditions and scriptural legends we know
from brick tablets and other remains that weights and measures
in some form or other flourished in Babylonia and Egypt, and
that the systems of the two countries doubtless had a common
origin. Although it cannot be definitely proved it is likely that
this origin was Babylonian, and much that has been written on
ancient metrology is based on this view. Hommel, in speaking of
the Babylonian metrology,1 states that from it " admittedly all
the ancient metrological systems (that of ancient Egypt included)
were derived." This is also the opinion of Dr. Brandis.2 Assum-
ing such to be the case, we are brought at once face to face with
a great diversity of opinion on the point as to whether a well-
developed and scientific system of weights and measures existed
in Babylonia, from which were derived the weights and measures
of the adjoining nations, and which, through trade and commerce,
spread over the then civilized earth, or whether various systems
of weights and measures came into existence separately in
different countries and gradually, with the development of civi-
lization and under similar conditions, spread abroad and became
more or less assimilated. The first is the point of view of
Boeckh 3 and the members of a distinguished school of Conti-
nental archaeologists and metrologists, and from available
monumental and literary remains with endless patience and
ingenuity they have evolved theories so scientifically constructed
that they excite admiration if they do not convince. On the
other hand there are a number of students of archaeology who
dispute the scientific basis on which such systems are constructed,
and deny that requisite knowledge and mental ability for such
scientific reasoning and construction was possessed by these early
^ee article "Babylonia," Hastings' Dictionary of the Bible (New York, 1903),
vol. i. p. 218.
2 See J. Brandis, Das Mum- Maass- und Gewichlswesen in Vorderasien bis auf
Alexander den Grossen (Berlin, 1866).
3 Boeckh, Metrologische Untersuchungen iiber Gewichte, Miinzfmse und Masse des
Alterthums (Berlin, 1838).
12 EVOLUTION OF WEIGHTS AND MEASURES
peoples. They claim that weights and measures from some
early body measures and natural standards developed according
to the needs of the people and depended on widely understood
ratios and rules of exchange rather than on any scientific
basis.
In considering the first point of view it is necessary to assume
that considerable mathematical and astronomical knowledge was
possessed by the ancient Babylonians and was used by them in
standardizing their weights and measures. In other words, from
ancient and arbitrary measures, doubtless of the body, they
developed such a system as was early required by the demands
of their scientific work in astronomy and their active building
operations. As measuring is essential to all scientific work, it is
not to be doubted that its importance was thus early recognized,
and in conjunction with their system of numerical notation a
permanent system was arranged. This was also brought into
direct relation with their astronomical' work, which was by no
means inconsiderable for these early times. In the course of
their observations it was ascertained that at the equinox the
apparent diameter of the sun on the horizon was ^-J-^ of the half
circle. Furthermore, by using a water clock, where water was
allowed to flow through a small orifice from one jar into another, it
was found that the amount received in the twelve hours between
sunrise and sunset was 360 times as much as when the sun was
traversing a distance equal to its own diameter or two minutes of
time.1 This afforded an accurate method of measuring time, and
formed the foundation of the sexagesimal system which was the
underlying principle of all Babylonian metrology and harmonized
perfectly with their system of numeration. This idea naturally
involved the division of the circle into 360 degrees, or rather 720
parts, which has continued to the present day, and the important
geometrical fact that the radius is equal the chord of one-sixth
the circumference was also well known at this time.2
1L. Ideler, " Ueber die Sternkunde der Chaldaeer," Abhandl. der k. A had.
Wissenschaft in Berlin, 1814-1815, p. 214. Referring to Cleomedes Cyclom.
(On the Circular Theory of the Heavenly Bodies), 1. 11. p. 75 ed. Balfor ;
Proclus Hypotyp. p. 41 (ed. Basil. 1540-4) ; Pappus, especially in his Com-
mentary on the Fifth Book of the Almagest of Ptolemy.
2Hommel, article "Babylonia," Hastings' Dictionary of the Bible (New York,
1903), vol. i. p. 219.
THE SCIENCE OF METROLOGY 13
By some authorities it was believed that the water jar referred
to above was also used as a measure of capacity, and that it was
divided on a duodecimal basis corresponding to the hour division.
It was then assumed that from a cube equal to such a volume
the unit of length was derived by taking the length of one of its
edges, which was the Babylonian foot, and bore a natural relation
to the cubit. This unit of volume when filled with water gave
the Babylonian talent, from which other units of the same name
were derived. This theory, however, which was supported for
many years, has been abandoned, and it is believed that the unit
of weight was derived from the unit of length, just as is done in
the modern metric system.
The relation of numbers and linear distances in Babylonian
measures is best derived from a study of the Senkereh Tablet,
which dates back to about 2500 B.C., and was discovered in 1850
in a small Arab village on the site of the ancient city of Larsam
or Larsa. It is now in the British Museum, and affords con-
siderable information as to the Babylonian measures and the
methods of computation. It is a clay tablet, on one side of
which are the fractions and multiples of the ell or cubit, and on
the other are the squares and cubes of the cubit from 1 to 40.1
This tablet has received the attention of a number of scholars,
including the late Professor Eawlinson, and the sexagesimal
character of the measures has been clearly demonstrated. In
connection with the scale of Gudea, to be described a few lines
below, it has been examined by the Rev. W. Shaw-Caldecott, who
concludes that " The breadth of the hand-palm conventionalized
was the fundamental of all length measures," and " That there
were three ell (cubit) lengths in simultaneous use, each probably
in a different kind of trade like our own Troy and avoirdupois
weights." 2
1Hommel, article " Babylonia," Hastings' Dictionary of the Bible (New York,
1903), vol. i. p. 218.
2 Shaw-Caldecott, "Linear Measures of Babylonia about 2500," p. 263, Journal
Royal Asiatic Society, 1903, London. In this article the characters on the
tablet are reproduced. See also R. Lepsius, " Der Baby lonisch- Assy rischen
Langenmasse nach der Tafel von Senkereh," in the Abhandlungen der
Kbniglichen Akadernie der Wissenschaften %u Berlin, 1877. With this article
is printed a photographic reproduction of the tablet, together with a recon-
struction.
14 EVOLUTION OF WEIGHTS AND MEASURES
Accordingly from the tablet Mr. Shaw-Caldecott derives the
following units and proportions :
Line - - = y^ of a palm.
Sossus - - - =-gL
Twentieth of a palm - = -^ „
Twelfth of a palm - = t? »
Third of a palm, or digit = ^ „
Palm.
Small ell (cubit) - =3 palms.
Medium ell (cubit) - = 4 palms.
Large ell (cubit) - =5 palms.
Small reed - = 4 small ells (cubits).
Medium reed - = 6 medium ells (cubits).
Large reed - = 6 large ells (cubits).
While the Senkereh Tablet establishes the ratios between the
various units yet it does not afford any' information as to their
absolute value, and for this recourse is had to a tablet forming
part of a statue discovered in 1881 at Telloh in southern
Babylonia, not far from Senkereh, by M. E. de Sarzec, and
now in the Louvre.1 It dates from about the same period as
the Senkereh Tablet, and represents King Gudea in a position
of prayer, and holding on his knees a slab of stone on which
is engraved the ground plan of a palace, a graving tool, and a
double line, the latter being cut near the outer edge and being
crossed by a number of indentations or cuts. This unmistakably
is a scale, and, furthermore, it is the oldest scale that has been
discovered up to the present time. By assuming that it is
the same size as the scale of linear measures then in use, and
by applying the proportions obtained from the Senkereh Tablet,
it is possible to obtain the lengths of the various units in terms
of modern equivalents, preserving the decimal and duodecimal
division characteristic of the Babylonian arithmetical system.
Thus we have the handbreadth or palm equal to 99-99*6 mm.
(3*9-4,l inches), and the cubit composed of five handbreadths
1 E. de Sarzec, De'couvertes en Chaldee, 1884-1889, PI. 15. See also Shaw-
Caldecott, loc. cit. See also Toy, " The Book of the Prophet Ezekiel " (Part 12,
Sacred Books of the Old Testament, "Polychrome Bible") (New York, 1889),.
Notes, pp. 179-180 for illustrations and description.
THE SCIENCE OF METROLOGY 15
equal to 495 mm. (19*483 inches), and also in early and wide-
spread use a double cubit twice this length or 990 mm. (38*976
inches). This latter unit is of interest on account of its close
approximation to the modern meter of 1000 mm., and also on
account of the fact, first discovered by Lehmann, that it is almost
exactly the length of the second's pendulum for the latitude of
Babylon (31 degrees north, at which point the theoretical length
of a second's pendulum would be 992*35 mm.). Consequently
he argues that the theory of the pendulum must have been
known to the early Babylonians, who doubtless derived it from
the plumb-line, which must have been employed in their
building operations.1 This fact, however, cannot be regarded
as more than a mere coincidence, and while it is most
interesting it is not considered possible that such an important
physical principle should have been known at so early a day
and then allowed to lapse from human knowledge until the
time of Galileo.
Multiplying the great cubit by 6 the " reed " was obtained,
and by taking 12 great cubits the gar. To form the ush or
stadion 60 gar were required, and 30 ush made a parasang or
kasbu, which was equivalent to about 21 kilometers. These
longer linear measures are again connected with the measure
of time, as 360 great cubits represented the distance an average
walker could accomplish in four minutes, while the great kasbu
of 21,600 cubits was the distance traversed during a night watch
of four hours or J of a day, and the small kasbu would be one
half of this distance.
Measures of area constructed by squaring the linear measures
are also claimed for the Babylonians, and here again the sexa-
gesimal ratio was preserved ; thus 180 she made a gin, which was
possibly equal to a square cubit. A " garden " (sar) was com-
posed of 60 gin, and 1800 gardens formed a "field" (gan). But
the Babylonians, in common with other Asiatic nations, also
employed for measuring land the amount of seed required to
1 Lehmann, p. 89, " Ueber das babylonische metrische System und dessen
Verbreitung, " Verh. der Physikalischen Gesellschaft zu Berlin (Berlin, 1890), vol.
viii. pp. 81-101 ; also in abstract, pp. 167-168, vol. lxi., Nature (London, 1889).
In this connection a paper by the same author, " Alt-babylonisches Maass und
Gewicht und deren Wanderung," Zeitschriflfur Ethnologie (Berlin, 1889), pp. 245-
328, may also be consulted with profit.
16 EVOLUTION OF WEIGHTS AND MEASURES
sow a field, and statements based on this idea are found in many
old Assyrian documents.1
The Babylonian capacity measures started with a cube whose
edge was a handbreadth in length (99-99*6 mm.), and which
when filled with water gave the unit of weight, the great mina,
which, occupying as it does almost the volume of a cubic deci-
meter, would correspond quite closely with the modern kilogram.
Such a capacity measure was known as the ka, and was nearly
the equivalent of the modern liter. As multiples of the ka
there was the gur, which was composed of either 360 or 300
of the smaller units, there being not only two such gurs but
a third divided into 180 parts and based on a double ka, from
which the Hebrews probably obtained their kor, which they
divided into 180 kab. Likewise in the subdivision of the
Babylonian measures there was the gin or ^ of a ka, which
in the Hebrew system was paralleled by the hin.
The relation between the capacity and' weight we have already
seen in the case of the great mina, which weighing, as it did,
between 982*4 and 985*8 grams giy^s a noticeably close approxi-
mation to the modern kilogram. \This great or heavy mina was
composed of 60 shekels, each of 3(T0 she or grains of corn, thus
combining in a system of weights two classes of natural units.
The greater weight was the talent composed of 60 minas. \ Such
a system would have been simplicity itself, were it notmr the
fact that several systems of weights, just as of linear measures,
are found employed at the same time. There was a light mina
which weighed one half of the heavy mina, and in fact
whole light and heavy systems standing to each other in the
ratio of 1 : 2 are believed to have existed, of which representative
weights have been found. Furthermore, as gold and silver,
whose values were in the ratio of 40 : 3, were used as currency,
other systems designed to accommodate both weight and value
arose, and there was a mina of gold which was composed of
50 units, each a shekel or g1^ of the weight mina. Then there
was a silver mina which weighed about ^ more than the Baby-
lonian mina of weight, while there was a Phoenician mina which
was also divided into 50 units, which made the whole equal to
J$$ of the original weight mina.
*C. H. W. Johns, Assyrian Deeds and Documents (London, 1902), vol. ii.
pp. 219-220.
THE SCIENCE OF METROLOGY 17
The subject of Babylonian units of weight is one of consider-
able complexity on account of the fact that weight and currency
had so intimate a relation and that gold and silver were both
standards. Furthermore, there was doubtless legislation stan-
dardizing certain other weights so that discrepancies would be
found on that score.
Having considered such a carefully erected structure we must
now discuss briefly the position of those that would demolish
utterly any such scientific arrangement and basis for ancient
weights and measures, and more particularly any connection
between the two. We are called upon to proceed further along
the lines indicated in the beginning of this chapter, and to
observe that the use of weights and measures accompanied the
gradual development of civilization, and that exactness in either
the determination of units of measure or in the preservation of
standards was no more characteristic of the twentieth or thirtieth
century B.C. than it was of the second or third. Although the early
Babylonians may have known how to divide time on a sexa-
gesimal basis and to observe eclipses, yet so simple a mathematical
process as obtaining area by multiplying length and breadth
together seems to have been unknown according to a study of
their literary remains, since for the measurements of land areas
the unit was not a square, but a strip of uniform width.1
Furthermore, the extensive use of the amount of seed required
superficial measures. The most strenuous objection has been
made to any systematic relation and connection between weights
and measures, and this feeling on the part of continental scholars
is considered due to their intimate knowledge and use of the
metric system, which acquired by them so readily would doubtless
suggest the possibility of the employment of its fundamental
features by the ancients. Why several thousand years should
intervene before the mind of man would return to such devices,
it is difficult if not impossible to explain, and like many other
phenomena considered now so simple, it is most natural to
assume that it was known to the ancients, yet at the same time
it is impossible to prove it. Thus any such relations must be
entirely hypothetical, and the only arguments to be advanced in
1 C. H. W. Johns, Assyrian Deeds and Documents (London, 1902), vol. ii.
pp. 219-220.
B
18 EVOLUTION OF WEIGHTS AND MEASURES
their support must be founded on circumstances which are pro-
bably mere coincidences, and doubtless most delusive. Professor
Flinders Petrie, in speaking of this subject, says : 1 " All that
can be said therefore to the many theories connecting weights
and measures is that they are possible, but our knowledge at
present does not admit of proving or disproving their exactitude.'*
Though this was written some years ago, nevertheless it is fair
to say that there has been no discovery or research that would
warrant any different expression from one holding Mr. Flinders
Petrie's views. According to another leading authority, the
Kev. C. H. W. Johns, who has carefully examined many literary
remains of the old Babylonians, there is not afforded by these
documents any ground for believing in any connection between
Babylonian measures of length and weight, while to him
Lehmann's idea of the double cubit derived from the second's
pendulum seems quite ridiculous. According to Bidgeway,2
considering the Hindus as an ancient people of culture, with
whose literature we have some acquaintance, we find that
" though they were clever mathematicians, yet they fixed their
standards of weights by natural seeds in the good old primi-
tive fashion, and did not make the slightest attempt to find
a mathematical basis for their metrological work."
In short, from this point of view the situation for the
Babylonians, and indeed for any other nation whose claim
for a similar priority should be advanced, may be summarized
as follows : The Babylonians in common with other nations
from body measures and seeds of grain or other plants developed
such systems of measurements as sufficed for their wants; their
standards were arbitrary and changing, but since they were
the leading people of this part of the world as regards culture,
their measures were impressed on their neighbors, and especially
on the Phoenicians, by whom as the chief traders of this period
of antiquity they were spread abroad. There is no reason to
believe that the weights were preserved in any kind of purity,
nor is there any reason to see why this should have occurred,
and when we consider the variation in weights and measures
aW. M. Flinders Petrie, article "Weights and Measures," Encyclopaedia
firitannica, 9th ed. vol. xxiv. p. 482.
2Ridgeway, Origin of Metallic Coinage and Weights, Cambridge, 1892, p. 178.
THE SCIENCE OF METROLOGY 19
during more recent centuries with their scientific men and
methods, their mints and their standards, not to mention
government regulation, as exampled, say, in Great Britain, it
is not natural to believe that those ancient units could have
been fixed to any basis with scientific exactness. Such mere
coincidences as that a cubic foot of water weighs 1000 ounces,
and that a British imperial gallon of water at temperature of
maximum density weighs ten pounds, if put back into the past
would form a far better basis upon which to form decimal
and other systems than many of the facts that have been
employed by scientific metrologists.1
As an argument of this kind depends largely upon quoting
authorities, and dealing in detail with apparent and actual
inconsistencies, it is manifestly impossible to do justice to it in
these few paragraphs ; but reference to Johns and Eidgeway
in the volumes quoted will amply repay the student interested
in this phase of archaeology and metrology, as by both authors
the^i-ase is stated most ably and critically.
{ The Jews, unlike their neighbors in Babylonia and Assyria,
\iere not a people of scientific tastes, and their weights and
measures were derived largely from the nations whose territory
they adjoined, consequently it is not natural to expect much
uniformity of weights and measures among them. Indeed, there
are indications that there were at a single time among the
Israelites as many as three different and distinct units of weight,
Babylonian, Syrian, and Phoenician, and in each case there was
both a heavy and a light system standing towards each other as
two to one. Undeniably there were Egyptian influences on the
Hebrew weights and measures, but far more is due to Babylon,
as the civilization of that country was predominant in Canaan
up to the fifteenth century B.C. according to records in the
Tel-el-Amarna correspondence, and this predominance carried
with it undoubtedly the Babylonian weights and measures. By
the eighth century B.C., however, the Israelites had a legal system
of weights and measures, put long before this they were
accustomed to their use, "as when Abraham bought the field of
Ephron he "weighed to Ephron the silver" (Gen. xxiii. 16).
1 Flinders Petrie, article "Weights and Measures," Encyclopaedia Britannica,
9th ed. vol. xxiv. p. 482.
20 EVOLUTION OF WEIGHTS AND MEASURES
In fact, the Israelites became so accustomed to the use of the
balance and of measures that they began to employ false weights
and wrong measures, with the result that not once but many
times1 their prophets and teachers are forced to emphasize honest
dealing in matters of measurements and the weighings of daily
life. The chief unit of length of the Hebrews was the cubit, ^
and with it were employed the usual body measures, such as
finger breadths or digits, palms, spans, and fathoms and reeds.
For these measures we have practically no data for determining
their equivalents, and Professor A. E. S. Kennedy expresses the
opinion " that reliable data for the exact evaluation of the
Hebrew cubit do not exist."2 In fact, values from 16 to 25*2
inches have been proposed for this unit, and by many it is
believed that there were two cubits, one the " cubit of man "
of six handbreadths, and also " a cubit and an handbreadth " or
seven handbreadths, which was used in the construction of the
temple (Ezekiel xl. 5). This would correspond to similar cubits
of the Egyptians, and there is reason for believing that the
weights and measures of the two nations were intimately con-
nected, if not quite similar at the time of the Exodus, but like
many other points in metrology it is not possible to bring
forward absolute proof. For the measurement of area the
Hebrews employed generally the amount of seed required to
sow the land, or the amount of ground that could be ploughed
by a yoke of oxen, the latter unit being the zemed, which in the
Old Testament is translated by acre.3 This is thought to be an
area equivalent to the Egyptian aroura, which was a square 100
cubits on each side.
The capacity measures of the Hebrews for both wet and dry
commodities were arranged upon a systematic basis which has in
not a few cases been obscured by imperfect translation in the
, English Bible.TThe relation of the different measures is expressly
stated in Ezekiel (xlv. 11 et seq.), where we learn that the ephah
and bath were one and the same unit, the former being used for
1 Leviticus xix. 35 et seq. Deuteronomy xx v. 13-16. Ezekiel xlv. 9-14. Amos
viii. 5. Hosea xii. 7. Micah vi. 10. Proverbs xi. 1, xvi. 11, xx. 10.
2 Kennedy, article "Weights and Measures," Hastings' Dictionary of the Bible
(New York, 1903), vol. v. p. 907.
3 1 Samuel xiv. 14 and Isaiah v. 10.
vy
THE SCIENCE OF METROLOGY 21
dry measure and the latter for liquids. This unit was one-tenth
of the homer, a dry measure, and its liquid equivalent was the
kor. One-third of the ephah gave the seah, which was divided in
half and formed a dry measure equivalent to the liquid hin.
One-tenth of the ephah gave a dry measure known as the oner,
while the next smaller unit, used for both dry and liquid
measure, was the kab, which was T-|^ of the homer or kor. * The
fourth of the kdb gave the log, the smallest liquid measure. I By
taking the ephah-bath as equal to 36*92 liters, or 65 (British)
imperial pints, a value derived from a study of Greek and
Hebrew literature, the modern equivalents can be approximated,
though this equivalent is variously stated from 3 6 '3 7 liters to
40*5 liters.
In considering the Hebrew units of weight we must bear in
mind what has been stated about the Babylonian units and their
fundamental proportions, where the talent was equal to 60 minas,
each composed of 60 shekels, or in the case of the gold mina of
50 shekels. There was the heavy and the light systems, stand-
ing in the ratio of 2:1, and, as we have said above, systems
based on Babylonian, Syrian, and Phoenician standards. Here
of course it must be remembered that the units of weight were
also units of currency, and to this fact is dudn no small degree
much of the variation in the standards. The shekel was for the
Hebrews the principal unit, and in the three different systems
mentioned from literary evidence and actual weights the follow-
ing values have been assigned :
Babylonian unit, - - - 252 grains.
Syrian unit, - - - -320,,
Phoenician unit, - - 224 „
The Hebrews' weights without doubt were not preserved in
anything like purity, and besides showing the effect of their
Babylonian origin, in later times there are evidences of Persian,
Greek, and Boman influences, so that our only means of iden-
tifying them consists largely in the connections established by
the later Hebrew and the Greek and Latin authors. The
weights of the Bible have received considerable study, and the
only warrant for dismissing the subject here so summarily is
that each separate phase demands detailed treatment and a
i
22 EVOLUTION OF WEIGHTS AND MEASURES
critical examination of authorities. Furthermore, the absence
of positive conclusions which can be stated definitely relieves
us of the necessity for fuller discussion in this brief historical
skatch-1
In the study of Egyptian measures there is considerable data *
for the metrologist, which is in the form of literary remains, such
as papyri, monuments of one form or other from the Great Pyra-
mid of Ghizeh to wall carvings, and actual wooden and stone
scales. In the main there is little variation from the measures
of Babylonia and many points of similarity both in the weights
and measures and in the etymology of the words expressing them
are seen, which indicate a common origin for the weights and
measures of both nations, and aid in substantiating any theory
based on the assumption that there was a definite parent systeml
There is a correspondence between the royal or building ciiDit of
seven palms and 28 digits which has been constructed from the
measurements of temples and other . buildings in Egypt and
the so-called sacred or building cubit of the Babylonians. Actual
representatives of the former have been found in the nilometer
cubit of Elephantis, and the wooden scale of Amenoemopht from
the necropolis at Memphis, and other scales both wooden and
stone.2 A mean value obtained from actual scales and measure-
ment gives for the modern equivalent of the cubit 525 mm.
or 20-63 inches.
With this royal cubit was also used a natural or common
(short) cubit which was of the length of six palms, and cor-
responded to the Greek cubit. The Egyptians employed the
various subdivisions on the basis of the body measures, but they
do not seem to have used either the foot or the fathom. All of
these can be found expressed in their hieroglyphics, and are found
in many of the ancient papyri. For long measure there was the
1 For further information and detailed references the following authorities may
be consulted : Kennedy, article " Weights and Measures," in Hastings' Dic-
tionary of the Bible (New York, 1902), vol. v. p. 901 et seq. ; G. F. Hill, article
" Weights and Measures," in Encyclopaedia Biblica (New York, 1903), vol. iv.
p. 5292 et seq. These and allied articles contain full and detailed bibliography.
See also C. R. Conder, "Hebrew Weights and Measures," Palestine Exploration
Fund Quarterly Statement, 1902.
2 For description and illustrations, see Lepsius, Ueber die alt-aegyptische Elle
und ihre EintheUung (Berlin, 1865).
THE SCIENCE OF METROLOGY 23
khet, which was equal to 100 cubits, and was represented by a
hieroglyphic of a coil of cord, as undoubtedly a line and reel were
used for such measurements, just as Ezekiel (xl. 3) speaks of a
"" flaxen line" and "measuring rod" being used in measuring the new
temple, and Jeremiah (xxxi. 32) mentions the use of the " measur-
ing line" in surveying land. For very long distances the Egyptians
had a measure, the ater, equal to from 30 to 60 or more stades
and known to the Greeks as a schoenus, but it is expressly stated
by Strabo that it varied in different parts of the country. It is.
of some importance, however, as it figures in geographical descrip-
tions of Egypt, and has been actually found marked on the
Memphis-Faium road.1 The Egyptians had a series of square
measures with a chief unit in the set equal to the Greek aroura
and comprising a square, a khet, or 100 royal cubits on each side,
the latter unit forming the basis of land measurement. For
capacity the principal measure was the hekt, which was equal to
-g1^- of the cubit cubed, while for corn there was employed the
khar ("sack") of 20 hekt until superseded by the sack of 16 hekt
or the Greek medimnus, at or before the XVIII. dynasty. After U
the Macedonian conquest the latter measure was halved to form
the artdba, doubtless to conform with a measure introduced from
Persia. Then there was the henu or ^ of the hekt, used both
for solids and liquids, as well as numerous other measures.
According to Griffiths, whom we have followed in this description
of Egyptian weights and measures,2 the Egyptian measures were
not derived from a cubit or fraction of a cubit cubed, but it is
probable that the cubic idea was introduced a considerable time
after the measures had been quite definitely fixed by custom.
In striking contrast to the many allusions to measures that are
found in the early papyri there is a lack of information as regards
weights. That weights existed and were used is known from a
large number of weights that have been discovered, and from the
blinders Petrie in Encyclopaedia Britannica, 9th ed. vol. xxiv., article
"Weights and Measures," p. 483. Also id., Season in Egypt, pi. xxvi. (London,
1888).
2F. L. Griffiths, "Notes on Egyptian Weights and Measures," Proceedings
Society of Biblical Archaeology (London), vol. xiv. p. 403 et seq., 1892. In this
paper will be found the various hieroglyphics and a full explanation of their use.
See also a continuation of this paper by the same author in same Proceedings,
vol. xv. p. 301, 1893.
24 EVOLUTION OF WEIGHTS AND MEASURES
fact that balances are shown in the decorations of the tombs of
the V., XI., XII., and XVIII. dynasties. In fact, the earliest
known weight is inscribed with the cartouche of Chufu (IV.
dynasty), the builder of the Great Pyramid at Ghizeh, whose
date was approximately 4000 B.C.
The use of the balance in the earliest times was probably con-
fined to exchange of gold and silver, and it doubtless was
invented for this purpose. But one reference is found to weights
before the XVII. dynasty, and only gold, silver, copper, and lapis
lazuli were weighed even at that time, as no mention of weight is
made in the so-called medical papyri, where it would be natural
to find such an allusion were weights in current use. Their
application increased slowly, and by the time of the Ptolemies,
incense, honey, and drugs, as well as metals and precious stones,
were weighed. About the time of the XVII. dynasty the
deben or uten, a weight of 1400-1500 grains, and its tenth part,
the kiti (also called Jcat) are found to, be the only recognized
units of weight in the various documents, but there have been
found a wide variety of actual weights, which it is quite impos-
sible to identify either with any system or among themselves,
and which serve to embarrass the investigator.1
Later the units of weight in widespread use were the talent,
the mina, and the shekel, as in other ancient nations, but con-
siderable diversity is shown, though in general plan much the
same division was followed as for the weights of the Babylonians
and Hebrews already described. By some authorities the basis
of the Egyptian unit of weight is considered to be a cubic
volume (the cubic foot or cubit) of water, but at all events there
were also various foreign influences, such as Greek and Asiatic
units of weight, which produced a certain amount of confusion,
and prevented any universal and single system. Under Ptolemy
Lagos (d. 283 B.C.), however, certain reforms of weights and
measures were effected that resulted in perpetuating the old
Egyptian system, and the talent weights thus defined were
known subsequently as the Alexandrian talents. These were
1 Flinders Petrie, article "Weights and Measures," Encyclopaedia Britannica,
9th ed. vol. xxiv. p. 486. Griffiths, loc. cit. p. 435, and vol. xv. p. 307. A. E.
Weigall, "Some Egyptian Weights in Professor Petrie's Collection," Proceedings
Society Biblical Archaeology (London), vol. xxiii. p. 378, 1901.
THE SCIENCE OF METROLOGY 25
of two classes, each of which were divided into 60 minas of
50 shekels or 100 didrachms each, but the greater Alexandrian
talent of copper or brass weighed just twice as much as the
smaller or lesser Alexandrian talent of silver. The former was
divided into 125 pounds by the Eomans when they occupied
Egypt, while the mina derived from the lesser talent was
divided into 12 ounces (unciae), and weighing as it did 5460'
grains, it became the predecessor of the series of European
pounds of which the Troy pound is a type. From one of these
ounces, if we may believe a Syrian authority, Anania de
Schiraz, who wrote in the sixth century, by taking the T\±
part the carats or diamond weight was originally formed.1
In Greece the fundamental unit of length was the foot, and
while we find the cubit, yet it is the foot that plays the principal
part. The same unit, namely, the Olympian foot, was found
throughout Greece, though, of course, there was necessarily
considerable divergence from any one value at different times
and different places. A clue to the actual length, however, is
found in the ruins of the Parthenon, where the main hall of
the Temple of Athena is called, according to Plutarch,2 Heka-
tompedos (one hundred feet), and measurements show that it
was 100 Attic feet in breadth by 225 in length, these numbers
being derived from the ratio of the breadth to the length, and
giving an Attic foot equal to '30828 meter or 12 '1375 inches.
One hundred times the foot gave the plethron, which was
squared and used as a measure of area. The Greek cubit, or
1-J- times the foot, closely resembles the natural cubit rather
than the sacred or building cubit of the Babylonians and Egyp-
tians, and four of them made the orguia or fathom, that is the
distance between the tips of the fingers when the arms were
extended. This multiplied by 100 gave the stadion, originally
the distance that a strong man could run without stopping for
breath, and then fixed as the length of the Olympian stadion or
athletic track, which was 600 feet in length.3 This stadion was
1 H. W. Chisholm, The Art of Weighing and Measuring (London, 1877), p. 42.
2 Plutarch, Pericles, 13.
3Hultsch, Griechische und Rbmische Metrologie, 2nd ed. (Berlin, 1882), p. 33.
This will be found a standard authority in classical measures, and will give
text references to all authorities. On it are based most of the statements in
the pages devoted to Greek and Roman metrology.
26 EVOLUTION OF WEIGHTS AND MEASURES
about one eighth of the Koman mile, and this ratio, as well as 8-^,
is used by Strabo and Polybius.
It was most natural that the measures of Greece should pass to
Home, and we find between the two a close connection. The
principle of subdivision was duodecimal, and we find the Greek
foot introduced as a unit of length. It, as well as the as, or unit
of weight, was divided into twelve unciae, whence our English
words inch and ounce. Among the other measures of length
employed by the Eomans was the palmipes, or foot and hand-
breadth ; and the cubitus (cubit), or, as it was also known, the
ulna, from which is derived the French word aulne and the
English ell. The passus or unit of itinerary measure was
equivalent to 5 Eoman feet, and when multiplied by 1000 gave
the millia passuum, from which was derived the mile as subse-
quently used in Britain and elsewhere. The passus was a double
step or gradus, and was the distance covered from the time when
one foot was taken from the ground until it was placed down
again. For architects and surveyors there was a unit ten feet in
length known as a pertica or decempeda, and the square of this
distance gave the unit of area employed in surveying, twelve
times which gave the actus or distance that a plow would
encompass in a single course, while the actus multiplied by two
would give the jugerum or Eoman acre (*6229 English acre).
Perhaps the foot is the most important of the Eoman measures,
as it not only extended throughout Europe as a fundamental
unit, but in some form it has survived almost everywhere until
supplanted by the meter. True, there were marked variations,
and the standards employed were most arbitrary, but the supre-
macy of the foot as the unit of length was maintained in Europe
until the nineteenth century. The connection of the Eoman
foot to that of Greece has already been shown, but attention
should be called to the fact that it gradually become shorter,
and in the time of Pliny it bore the relation to the Greek foot
of 25 : 24. There was also a foot of Drusus which was used
outside of Italy for measuring land, and became permanent in
the countries along the Ehine and Lower Germany. This foot
contained 13-|- Eoman inches or 13*1058 English inches, 332*6 mm.,
and doubtless came to Europe in some way from Asia Minor.
It is worthy of note that, besides persisting in the Ehine
THE SCIENCE OF METROLOGY 27
countries, it was adopted by the Belgic tribes, and by them
introduced into Britain, where it endured, as will subsequently
be shown, until the fifteenth century.1
Greece originally had as its standard of weight the heavier
Babylonian talent, or, speaking more exactly, this was in use
in Aegina, and thence extended into the Spartan States and to
Corinth, whose inhabitants being actively engaged in commerce
did much to spread its use. This talent was considered equal
to the weight of a cube of water whose edge was an Olympic
cubit, or 1^- times a Greek or Olympic foot. By diminishing
the Babylonian talent one-sixth, was obtained the Euboic talent
which nourished in Greece and especially in Athens before the
time of Solon. This latter ruler in order to release the people
from the usurers established by decree (c. 592 B.C.) a smaller
talent which amounted to § of the Babylonian talent, and
weights were derived from it which alone were lawful in Athens.
The close connection between money and weight then existing
must be appreciated, and we find in ancient writings that the
material of the talent when used as currency is mentioned, as a
talent of silver (the standard) or a talent of gold. The Athenian
talent was divided into 60 minas, each composed of 100 drachmas
containing each 6 obols or 48 ehalkus. There was a half mina
and a double drachma or didrachm, and also a gramma equal
to one third of a drachma or 2 obols, one third of which was a
lupine whose half in turn was a siliqua. The unit of liquid
measure in the Athenian system was the metretes (3 9 '39 liters),
which was subdivided into 12 chus or amphora, and so on on a
duodecimal basis. The metretes was -^ of a Babylonian cubic
foot. J The Attic unit of dry measure was the medimnos, which
corresponded to 1 -J- metretes or in modern equivalents to 52*53 -j
liters. It was divided into six hekteus or modius, each of which v'
was composed of two hemiekton or eight choinix. The choinix
was made up of two xestes, and two kotule formed a xestes.
The Roman unit of weight was the libra, or pound which
corresponded in money to the as, and was divided on the
duodecimal basis characteristic of the Romans. Thus the pound
(327*45 grams) was composed of 12 unciae, each of 4 sicilii, each
■of 2 drachmas, each of 33wri_pula, each of 2 obola, and each of
JSee p. 31.
r~
28 EVOLUTION OF WEIGHTS AND MEASURES
3 siliquae, these names surviving in modern apothecaries'
measure. Its connection by water with the amphora and thus
with the Greek measures will be given below, and may be
further explained by stating that while the Attic talent of
Solon was divided into 60 minas, the same weight of water
contained in the amphora was divided into 80 pounds, thus-
making 3 Attic minas equal to 4 Eoman pounds. Originally
the Eoman pound was established on the basis of the Aeginetan
weight, and was equal to T^ of the Aeginetan half mina,
this basis being used in the Eoman coinage.
As a measure of liquid capacity the Eomans had the amphora,
which was equal to a cubic footfand contained 80 librae (pounds)
of water. This was divided into 8 congii, each composed of
6 sextarii with further subdivisions. For dry measure one third
of the amphora or modius served as the unit, and was made up
of 16 sextarii. These measures harmonized with those of Greece,
inasmuch as the amphora was two thirds of the JUtic metre tes,
and the modius was one sixth of the medimnos.| In passing,
mention might be made of the fact that a foot derived theo-
retically from the amphora would not give a cube equal to
the amphora, but differing by as much as a twentieth part
and in some cases by as much as one twelfth, depending, of
course, upon the cubical contents of surviving examples, of which
there are several.1
The Eoman weights, measures, and coinage, by virtue of the
conquests and influence of the empire, found their way all over
Western Asia and Europe ; and with the decline of the imperial
power formed the foundation for local systems, but with the lack
of interest in science which soon began to characterize the age
and the general decline of culture, weights and measures were no
longer maintained in conformity with any system or with any
due regard to primary standards. Consequently there was a
distinct corruption of measures, and until the revival of experi-
mental science in the middleages but little attention was-
paid to the subject. Indeed, /all standards and systems were
practically neglected, and by the sixteenth century there was
virtually a return to the body measures throughout Europe.
1 Flinders Petrie, article ' ' Weights and Measures," Encyclopaedia Britannica,
9th ed. vol. xxiv. p. 486.
THE SCIENCE OF METROLOGY 29
__^- Breyious to the beginnings of European scientific investiga-
tion^there was, however, important work done by the Arabs, and
as measurement is an essential of all experimental science, it was
natural that they should have devoted much attention to the
subject, and included the discussion of measures in their writings.
It is quite certain that the measures of the Arabs owe their
origin to the old Babylonian measures, especially as their
philosophers were careful students of antiquity ; but it is evident
that while the measures were maintained they lost sight of the
underlying principles, and when it became necessary to define
them or refer them to standards, entirely new methods were
employed. In these an attempt was made to secure a natural
basis, and such fundamental units as a degree of the earth, hairs
of horses or mules, and grains of barley were used. Then, too,
the contact between the Arabs and the Egyptians had its effect,
and old and new measures were blended so that the absolute
value of the weights and measures is quite impossible to
determine, though by references to ancient authorities relative
values can be obtained in many cases.2 It was from the Arabs
that the Yusdruman pound of Charlemagne, for so many years
the standard of France, was obtained, and the idea of using
barleycorns for the measure of length, as was done subsequently
in England by statute.
In this connection mention might be made of a unit of length,
namely, the " black cubit," which figured in an important
measurement of a degree of the earth's surface executed in 830
A.D. by the astronomers of the Caliph Al-Mamun (713-833).
This measurement, made on the plains of Mesopotamia, is
generally spoken of in connection with similar measurements
made by Eratosthenes (c. 276 — c. 196 B.C.), the Alexandrian, as
they were the forerunners of later geodetic work, on which in
part the modern metric system was founded, it being of course
unnecessary to say that this and other ancient astronomers
believed in the spheroidal form of the earth. The " black cubit,"
1 About the earliest systematic works in Metrology in England are A Discourse
on the Roman Foot and Denarius and Origin and Antiquity of our English Weights
and Measures (London, 1745), by John Greaves (1602-1652), and De Mensuris
et Ponderibus Antiquis (Oxford, 1699), by Edward Bernard (1636-1696[7J).
2 See Boeckh, Metrologische Untersuchungen (Berlin, 1838), pp. 246 et seq.
30 EVOLUTION OF WEIGHTS AND MEASURES
however scientific the use to which it was put, was not due to
any particular metrological study, but, according to tradition, was
the length of the arm of a favorite black slave of the Caliph, and
has been said by Jomard to have been equal to 519*16 mm.1
The source from which the Anglo-Saxons derived their weights
and measures is not particularly certain, yet they early en-
deavoured to secure uniformity by enacting good laws,2 and in
this they were so successful that they were enabled to maintain
these weights and measures in their integrity despite the Norman
conquest.3 In fact, they were specially recognized and preserved
by a decree of William the Conqueror, which stated that " the
measures and weights shall be true and stamped in all parts of
the country, as had before been ordained by law." The stan-
dards of the Saxon kings which had been preserved at Winchester
were, however, removed to London, where they were deposited in
the crypt chapel of Edward the Confessor in Westminster Abbey,
which later became known as the Pyx Chapel, as here were also
preserved the standard trial plates for gold and silver coin used
at the trials of the pyx, or formal official assay of the coin of the
realm.4 With Winchester are associated the earliest Anglo-
Saxon weights and measures, and their authority as standards
is said to date back to King Edgar (reigned 958-975), who decreed
that " the measures of Winchester shall be the standard." The
unit of length was the yard or gird, which was identical with the
1 See Boeckh, Metrologische Untersuchungen (Berlin, 1838), pp. 246, 250-3.
2 Greaves, Origin and Antiquity of our English Weights and Measures (London,
1745), p. 68.
3 Bishop Fleetwood's Chronicon Preciosum (London, 1745), p. 27: "It was a
good law of King Edgar that there should be the same money, the same weight,
and the same measures, throughout the kingdom, but it was never well observed.
What can be more vexatious and unprofitable both to men of reading and practice,
than to find that when they go out of one country into another, they must learn
a new language or cannot buy or sell anything. An acre is not an acre ; nor a
bushel a bushel if you but travel ten miles. A pound is not a pound if you go
from a goldsmith to a grocer, nor a gallon a gallon if you go from the alehouse to
the tavern. What purpose does this variety serve, or what necessity is there,
which the difference of price would not better answer and supply ? "
4 See H. J. Chaney, Our Weights and Measures (London, 1897), pp. 120-121.
An interesting account of the Pyx Chamber together with a description of the
Jewel Tower, now the Office of the Standards, will be found in "The Story of a
Tower," The Art Journal (London, 1900), pp. 200-203 and 244-247.
THE SCIENCE OF METROLOGY 31
ell, and as late as the reign of Eichard II. (1377-1399) the words
virga or verge (yard) and ulna or aulne (ell) are found in the laws
and official documents in Latin or Norman French, as the case
may be, to denote the same unit of length. In addition to the
purely Saxon measures there were those which had been brought
by the Eoman, and which, though incommensurable with Saxon
measures, had survived and become assimilated with the older
measures. Among these were the mile, corresponding to the
Eoman millia passuum, the inch and the foot, which soon became
recognized as purely English measures and to have their own
fixed values. Then, in addition, when the Belgic tribes migrated
to Britain, they brought the Belgic foot of the Tungri, which
was -J- longer than the Eoman foot, and was used until the
fifteenth century.1 The average length of this foot was 13 '22
inches, and a yard formed by three such feet would be 39*66
inches, which would correspond most closely with the meter of
to-day, which is equivalent to 3 9 '3 7 inches. Such a yard existed
and was known as the yard and the full hand, and eventually
was suppressed by law in 1439. This was extremely unfortunate,
as had this yard been retained it would have ensured a corre-
spondence with the French metric system without the slightest
difficulty. Furthermore, we are informed that the old English
system was largely decimal, and had these features been pre-
served a vast improvement would have been worked in the
wretched system, or lack of system, with which the English-
speaking people have been afflicted for centuries.
In the Domesday Book (1086) we find the Saxon yard used a&
a unit of measure, and land thus measured is referred to as terra
virgata, and shortly afterwards, from the reign of Henry I.
(reigned 1100-1135), the tradition is current that the legal yard
was established from the length of that monarch's arm. \ In the
reign of Eichard I. (reigned 1189-1199) there were laws ' enacted
providing for standards of length constructed of iron and for
measures of capacity whose brims should be of this material also,
suitable standard measures to be kept by sheriffs and magistrates.2
1 Flinders Petrie, article "Weights and Measures," Encyclopaedia Briianuica,
9th ed. vol. xxiv. p. 484.
2 See Kelly, Metrology (London, 1816), p. 336. A brief and interesting account
of early history of British Weights and Measures, with summary of legislation.
V
v
32 EVOLUTION OF WEIGHTS AND MEASURES
CThe most important early English legislation was contained in
Magna Charta (1215), and laid stress on the principle of uni-
formity by providing that there should be throughout the realm,
one measure of wine, one of ale, and one of corn, viz., the quarter
■of London : and that it should be of weights as of measures]
This declaration of uniformity was considered so fundamental that
it was subsequently repeated in numerous statutes in essentially
its original form, and we find many acts passed as occasion
demanded to carry out its manifest intention. This naturally
involved the definition of the standards and measures, and from
time to time statutes are found which supply us with more or
less complete information about the measures of the period.
Thus, while we know that the unit of monetary weight was a pound
used from the times of the Saxon kings, yet we do not find it
•defined until the time of Henry III. (51 Henry III., stat. I. 1266),
when! the relation of the various weights and measures are given
by the following law, forming a part of the well known statute of
the Assize of Bread and Ale, where it' is stated, "that by the
■consent of the whole realm of England, the measure of our Lord
the king was made, viz., an English penny called a sterling, round
and without any clipping, shall weigh thirty-two wheatcorns in
the midst of the ear ; l and twenty pence do make an ounce, and
twelve ounces a pound: and eight pounds do make a gallon of
wine, and eight gallons of wine do make a bushel, which is tnV
eighth part of a quarter." Thus we have defined the ancient
Tower Pound, which, having the same weight as the old German
medicinal or apothecaries pound, is believed to have been derived
from the mina of Ptolemy or one-sixtieth part of the Lesser
Alexandrian Talent of silver, as it was but 63 grains lighter than
that weight. This was the earliest form of the British sterling
pound, and the division into 20 shillings of 12 pence each was
the same as is now practised, and in fact was the same as the
•division of the livre esterlin of Charlemagne, which was slightly
heavier (5666 Troy grains as compared with 5400, see p. 38).
In addition, the English monetary weights were connected with
those of Germany, based on the Cologne mark, by a mint weight
1,4 This pennyweight was equal to 22^ Troy grains, which is found to be the
average weight of existing coined silver pennies of the Saxon Norman Kings "
(Chisholm, Weighing and Measuring, London, 1877).
THE SCIENCE OF METROLOGY 33
substantially equivalent to the latter and equal to two-thirds of
the Tower pound. This was known as a mark, and was used for
denoting both the weight and value of silver under the Norman
kings.1 While the Tower pound was defined in terms of grains
of wheat, nevertheless it did not originally depend upon them,
and their inclusion in the English system of weights was doubt-
less due to French influences subsequent to the Norman Conquest,
as the French had doubtless derived this idea from Oriental
sources. With the Tower pound used for mint purposes, and for
the derivation of measures of capacity, as well as for precious
metals in general and drugs, there must be considered the com-
mercial pound {libra mercatoria), which is of almost as great
antiquity and of far more general use. It also is defined in a
statute of Henry III. (54 Henry III.) and was the weight of 25
shillings, or in other words equivalent to 15 ounces of the Tower
pound. Commercial pounds were used also on the continent
of Europe along with the Troy pound, and it is to one of
these, namely the French commercial pound of 16 ounces, that
we have to look for the source of the English avoirdupois
pound which soon supplanted the commercial pound in that
country.
The early English Tower and commercial pounds were forced
to give way before the French weights, the Troy pound and the
avoirdupois pound, whose use the more intimate contact following
the English victories in France at Poitiers and on other fields had
doubtless spread through the English realm. As to the source of
the Troy pound there is a difference of authorities, but it is usual
to credit it to the city of Troyes in France, and in support of this
view it is stated that associated with this city, a town of some
commercial importance, were a livre cle Troyes and a marc cle Troyes,
whose weights were comparable with the modern Troy pound.
Going back still further, it is possible to derive the Troy pound
from the Roman weight of 57592 grains, which was the 3-^5 of
the large Alexandrian talent. This weight, after the fashion of
the Romans, was divided into 12 ounces, and the original unit
and its division may possibly have survived. At all events the
Troy pound slowly made its way in England, and from as early
as the first year of the reign of Henry IV., when it was employed
1H. W. Chisholm, The Art of Weighing and Measuring (London, 1877), p. 55.
C
34 EVOLUTION OF WEIGHTS AND MEASURES
in an inventory of the Royal plate, it was increasingly used. In
1495, in defining the bushel and the gallon, Henry VII. made use
of the Troy pound, and in 1527 the Tower pound was formally
abolished as the legal standard at the Mint by an Ordinance
(18 Henry VIII.) enacting that " the Pounde Towre shall be no
more used and occupied, but al maner of golde and sylver shall
be wayed by the Pounde Troye, which maketh xii oz. Troye,
which excedith the Pounde Towre in weight iii quarters of the
oz." Likewise, as we have indicated, the avoirdupois pound was
adopted as a commercial pound, and formed of 16 avoirdupois
ounces, and composed of 7000 Troy grains, it is mentioned in
a statute (Tractatus Ponderibus et Mensuris) of Edward I.
(31 Edward I. 1303). From these origins the English Troy and
avoirdupois pound have descended in substantial integrity to the
present time, and such changes as have been made have been due
to the restoration of standards, and have been of a minute and
unavoidable character.
Many standards of weight were constructed based on these
fundamental definitions, and a number of them are still in exist-
ence, having been used on numerous occasions for deriving other
standards. In fact, one bell-shaped avoirdupois pound of the
Exchequer of the reign of Queen Elizabeth was continuously used
for this purpose from 1588 to 1825. This weight, which at the
time of its construction in 1588 was supposed to be equal to 7002
Troy grains, was found in 1873 to weigh 6999 grains of the
imperial standard pound.1
In 1758 a standard Troy pound was constructed and standard-
ized by Harris under authorization of an Act of Parliament, but
it was not legalized until 1824 (5 Geo. IV. c. 74). It was then
specified (§ 5) that in the event of the loss or destruction of this
standard, that it should be reconstructed by considering that a
cubic inch of distilled water at 62 degrees Fahrenheit, weighed in
air with brass weights, and at 30 inches pressure of the mercurial
barometer, should weigh 252*458 grains, of which the Troy pound
contained 57 60.2 This standard was destroyed together with
1 H. W. Chisholm, The Art of Weighing and Measuring (London, 1877), pp. 62
and 63.
2 This definition bound the unit of weight to the unit of length, which was then
considered fixed by its reference to the second's pendulum.
THE SCIENCE OF METROLOGY 35
the standard yard by the fire of October 16, 1834, when the
Houses of Parliament were burnt. To construct new standards a
Standards Commission was appointed in 1843, and for the unit of
weight the avoirdupois pound was taken as the basis. The new
standard was defined in terms of the lost Troy pound as given by
various existing standards, and was duly legalized in 1855 (18 and
19 Vict. c. 72). This standard pound will be more specifically
described when we come to discuss the subject of Standards in a
subsequent chapter.1
From the definition of the measures of capacity, given in the
Statute of the Assize of Bread and Ale referred to above, the
gallon and the bushel were obtained from the pound, using wine
as the measuring medium. This class of measures was one that
greatly concerned the government on account of the collection of
the excise duties, and there are numerous statutes defining or
regulating in one way or another the capacity and use of these
measures. On the basis of the early legal definition, however,
Henry VII. caused to be constructed a standard corn gallon and
a standard corn bushel, the former having __a capacity of 27 4 -\
cubic inches and the latter 2 150 J cubic inches. 1 These- standards
date from 1495, and are now in actual existence. The Win-
chester corn gallon, as the measure is known, was employed
until it was supplanted in 1824 by the imperial gallon, while its
companion, the Winchester bushel, which was similarly outlawed
in 1824 in favour of the imperial^ bushel in Great Britain, has
survived in the United States. | In 1601 we find the British ale
gallon with a capacity of 282 cubic inches duly recognized by
Queen Elizabeth/Jand there is extant an Exchequer standard
quart which bears this date and the royal initials and crown.
In the reign of Queen Anne the standard wine gallon was
defined by statute (5 Ann. cap. 27, 17) as " any cylinder 7 inches
in diameter, and 6 inches deep, or any vessel containing 231
cubical inches and no more shall be a lawful wine gallon."
Such a standard of the Exchequer dated 1707 is still extant. On
the reorganization of the weights and measures in 1824 the wine
gallon was abolished, but it was never supplanted in the United
1 Chas. Ed. Guillaume, Unite's et Etalons (Paris, 1893), p. 96. H. W . Chisholm,
The Art of Weighing and Measuring (London, 1877), pp. 69-81. W. H. Miller,
Philosophical Transactions (London, 1856), part iii.
36 EVOLUTION OF WEIGHTS AND MEASURES
States, and remains as the legal gallon. The British imperial
gallon, legalized in 1824 (5 Geo. IV. c. 74) to the exclusion of the
three former gallon measures, and which forms the basis of the
present British measures of capacity, instead of being based on a
given number of cubic inches, was taken as the volume of ten
pounds of pure distilled water at 62 degrees Fahrenheit. This
corresponds to 277*274 cubic inches. [JWith the gallon as the
unit of capacity for liquid measures, it was determined to derive
the imperial standard bushel or unit of capacity by taking a
volume equal to eight imperial gallons, or a volume corresponding
to 2218*192 cubic inches. )
Unlike the measures of weight and capacity, there have been
few changes in those of length from the times of the Saxons, and
the earliest surviving standards of length, those of Henry VII.
(about 1490), and Elizabeth (about 1588), vary scarcely more
than a hundredth of an inch from the present imperial yard.1
With the second of these standards there is also an ell rod of
45 inches, and a bar with a bed or matrix for both the yard and
the ell rods, but such an ell, which doubtless corresponded to the
French measure of cloth, does not appear in any statute or in
the records of the standards of this time. In fact, we find the
Anglo-Saxon measures of length perpetuated on the same basis
as is given in the statute of Edward II. (17 Edward II. 1324),
where there is a restatement in statutory form of what has since
become the well-known rule that three barley-corns, round and
dry, make an inch, twelve inches a foot, three feet a yard (ulna),
five and a half yards a perch, and forty perches in length and
four in breadth an acre.2
Consequently the general discussion that has been devoted to
1 See chapter x. on Standards, pp. 243-244.
2 See H. W. Chisholm, Seventh Annual Report of the Warden of the Standards,
1872-3 (London), pp. 25 and 34, English Parliamentary Papers, Reports from
Commissioners, 1873, vol. xxxviii. Id., Weighing and Measuring (London,
1877), pp. 51-53. George Graham, " Description of Standards and Use of Beam
Compasses," Philosophical Transactions (London, 1742-3), vol. xlii. pp. 541-556.
Francis Baily, Memoirs Royal Astronomical Society (London), vol. ix. 1836,
pp. 35-184. William Harkness, "The Progress of Science as Exemplified in the
Art of Weighing and Measuring," vol. x. Bulletin Philosophical Society of
Washington, D.C., published as vol. xxx. Smithsonian Miscellaneous Collec-
tions. The latter contains a good resume of British weights and measures as
well as a useful bibliography.
THE SCIENCE OF METROLOGY 37
the British measures of length has been mainly towards securing
standards of greater accuracy, or with the object of obtaining
either a decimal division or the adoption of the metric system.
With the exception of the act of 1824, which defined the yard in
terms of the second's pendulum, and provided in case of its loss
or destruction that it should be replaced on that basis, little
has been done in the way of legislative enactment save to
recognize and establish legally new standards of length. The
determination and construction of such standards, however, has
been of extreme importance, and has involved most careful and
accurate scientific work, so that for this reason the various British
standards and their development can best be treated in that
portion of the present volume devoted to this subject.1
While there have been for well over a century many and
earnest advocates of a decimal division of British weights
and currency, yet the net results of their labors and agitation
have been practically nothing other than to strengthen the
cause of the metric partisans. In fact, decimalization never
has progressed to the same point as in the United States, and
it is probable that the old weights, measures, and methods
will remain until supplanted by the metric system.2
Although the preservation of the French standards of measure
in the royal palace is recorded from the time of Dagobert (650),3
yet it is usual to trace back such measures as might properly
be considered as forming the national system to the time of
Charlemagne (768-814), since during his reign there was a
uniformity of weights and measures, and reproductions of the
royal standards were widely distributed over the realm.4 The
unit of length in this system was the pied de Roi, or royal
foot, representing, according to tradition, the length of the
foot of the monarch, and which, following the duodecimal
•
xSee chapter x. — Standards and Comparison.
2 For progress of Metric System in Great Britain, see chapter iii. pp. 98 et seq.
It is of course impossible in the present space to describe the various measures
of Scotland, Ireland, and other local systems. These will be found quite fully
described in Kelly, Metrology (London, 1816), and also in Chaney, Our Weights
and Measures (London, 1897), the latter containing also a description of the
various standards.
3 Paucton, Metrologie ou TraiU des Mesures, Poids et Monnoies (Paris, 1780), p. 8.
4 Ibid. p. 13.
38 EVOLUTION OF WEIGHTS AND MEASURES
division derived from the Komans, was divided into 12 inches
(police) of 12 lines, which in turn were composed of 12 points.
The French foot was longer than the English foot, being equal
to 12*79 inches of the latter, and considerably longer than the
ancient Eoman foot, which was 11*65 English inches in length.
In the French system there was also the toise or fathom of six
feet, and the earliest record of a standard of length dates back to
the Toise du Grand Chatelet, constructed in 1668, and based (though
five lignes shorter) on the ancient toise de magons of Paris, which
was doubtless as old as the times of Charlemagne.1 It is said
by La Condamine2 to represent one half the distance (12 feet)
between the walls of the inner gate of the Louvre. Subsequently,
copies of this were made, and the toise was used as the basis for
standards of linear measures, such as the Toise de Perou? There
was also the aune or ell, which, originally a double cubit, became
adopted as a unit of linear measure for cloth, and survived until
displaced by the meter. A standard Aune des Marchands,
Merciers et Grossiers, 1554, divided into halves, quarters, thirds,
sixths, etc., was preserved by that guild, and was the basis of
this unit. The aune of Paris corresponded to 46^ Eng. inches,
but it was never adopted in the latter country to any considerable
extent or authorized by law, though a cloth aune or ell of 45 in.
is found marked on the standard yard of Queen Elizabeth.4
For the origin of standards of weight in France we have to go
back to the Arabs, as the basis of the ancient French system is re-
puted to be an Arab yusdruma, which was sent by Caliph Al Mamun
(786-833) to Charlemagne. This yusdruma, or later Arab pound,
was the monetary pound or livre esterlin of Charlemagne, and
amounted to 5666 J grains, or 367*128 grams.5 It was divided into
12 ounces, or 20 sols, of 12 deniers, of 2 oboles of 12 grains, or
5760 grains in the aggregate, each grain weighing *063738 grams.
1 La Hire, Mem. de VAcad. Roy. des Sciences, 1714, pp. 394-400 (Paris, 1717).
2 La Condamine, Memoires de VAcad. Roy. des Sciences, 1772, 2nd part,
pp. 482-501 (Paris, 1776).
3 See chapter x. on Standards.
4 See chapter on Standards, p. 243. Also ante, p. 31.
5 The name "esterlin" was employed at one time in the French language to
signify "true," being equivalent to the modern Fr. word "veritable." It has,
however, disappeared from use, but has been retained in English, with the same
signification, in the form of "sterling," as, for example, "pounds sterling."
THE SCIENCE OF METROLOGY 39
The livre esterlin of Charlemagne was one and a half times the
weight of the marc of the monetary system which was established
between 1076 and 1093 by Philip L, who used 8 of the 12 ounces
of the former system for this purpose. This marc was doubled,
and made to consist of 16 ounces, by King John the Good, in
1350, and it was adjusted according to the weights of Charlemagne.
The weights of King John were known as the " pile de Charle-
magne," and were the French standards of weight until the
adoption of the Metric System in 1789.1 In this system the
livre poid de marc, or pound, consisted of two marcs or half-
pounds, 4 quarterons, 8 half -quarterons, 16 ounces, 32 half-ounces,
128 gros (drachme) or grams, 384 scruples, or deniers, 9216 grains.
There were also in France four other marcs duly and legally
recognized, viz., that of Kochelle, which was called English, equal
to 13 sols, 4 deniers, in terms of the livre esterlin; that of
Limoges, equivalent to 13 sols, 3 oboles ; that of Tours, equal to
12 sols, 11 deniers, 1 obole ; and that of Troyes and Paris, equi-
valent to 14 sols, 2 deniers.2
We have referred specifically to early measures only in Great
Britain and France, as throughout the rest of Europe there was
such great diversity until well into the nineteenth century that
little would be gained for our purpose by considering the dozens
of kingdoms, principalities, free cities, etc., each with their
separate systems. Local conditions and traditions everywhere
governed, and riolTonly in different countries in the same region
would there be different values for the same weights and
measures, but also in different towns of the same state.3 While
the names feet, pounds, etc., were quite universally employed, yet
they designated different quantities, and save for arbitrary
standards, possibly in many cases not even duly legalized, there
was no attempt at securing uniformity. A foot might be divided
1 Guillaume, p. 94, Les Unites et Etalons (Paris,
2 Quoted by Guillaume, p. 95, Les Unite's et Etalons, from Chronique de 1329
■environ.
3 "At the close of the last (eighteenth) century, in different parts of the
world, the word pound was applied to 391 different units of weight and the
word foot to 282 different units of length." T. C. Mendenhall, Measurements of
Precision. Such a list with British and metric equivalents may be found in
Barnard, The Metric System (Boston, 1879), pp. 348-360. The kilogram has
.superseded over 370 of the different pounds.
40 EVOLUTION OF WEIGHTS AND MEASURES
duodecimally, as was done by the Eomans, or, on the other hand,
it might be divided into nine, ten, eleven, or thirteen inches.
Then again the actual distance represented by a foot varied
from 9 to 18 inches, and equivalents are now known for many
different European feet.
As to the sources of these measures, we have to look to the
Eomans and to the East, as the former nation in its conquests
overran a great part of Europe, . and implanted its weights and
measures with more or less permanence, while the effects of trade
with the Orient and the intellectual influence of the Arabs
doubtless served to introduce new measures or to corrupt old
ones. Several mark weights soon became known as standards
for coinage and precious metals, notably that at Cologne, while the
Ehine foot enjoyed a pre-eminence in the neighboring countries.1
As practically no scientific work of a quantitative character was
done for many centuries, the influence of science in systematizing
and demanding exact standards of measure was not felt, so that
only the needs of trade, often of a most restricted character,
which could be satisfied by crude and imperfect systems, had
to be provided for. The lineage of many of the old European
weights and measures has been traced more or less satisfactorily
back to ancient times, but the subject presents little scientific
attraction, save to the historian or archaeologist and the student
of metrology.2 Lack of system prevailed, and apparently was
quite satisfactory, but gradually the minds of scientists and
statesmen became aroused to the importance of the subject and
the need of fundamental changes, and a rational systematization
was urged, which found its first substantial fruit in the develop-
ment in France of the metric system.
1 This Rhine foot defined in Prussia by law in 1816 was standardized by Bessel
in 1835-1838, and survived in that kingdom until the adoption of the metric
system. It is still (1906) the standard of length in Denmark.
2 An interesting summary of ancient and modern measures, which, however,
must be modified in many aspects, and considered in the light of modern
researches and theories, is contained with a wealth of bibliographical material
in Karsten, Allgemeine Encyklopddie der Physik, vol i. " Maass und Messen "
(Leipsic, 1869).
CHAPTER II.
ORIGIN AND DEVELOPMENT OF THE METRIC SYSTEM.1
While the inconveniences and difficulties attending arbitrary
systems of weights and measures were appreciated, nevertheless
philosopher and peasant alike submitted, and it took many years
for a feeling in favour of a rational and fixed system to develop.
Such a system at its best, as we have seen, would involve an
invariable unit derived from nature itself, which not only could
be reproduced readily, but was capable of being measured with a
1In this chapter detailed references have been given to authorities for
particular statements for the benefit of those who desire to pursue the subject
further. The history of the Metric System has been well summed up in a
treatise by M. Bigourdan (Le Systdme Me'trique, Paris, 1901), in which will be
found usually the text of all French legislation and the salient features of
discussion by lawmakers and scientists, as well as a complete bibliography.
There is also an excellent historical sketch, "Notice historique sur le Systeme
Metrique, sur ses developpements et sur sa propagation," contained in the
Annales du Conservatoire (Imperial) des Arts et Metiers, by General A. Morin
(Paris, 1870), vol. ix. pp. 573-640. This is a brief but excellent description of
the origin and development of the system by a member of the Committee of
Verification, director of the Conservatoire des Arts et Metiers, and a member
of the first International Commission. "A Historical Sketch of the Foundation
of the Metric System," by General Bassot, was published in the Annuaire pour
Van 1901, of the Bureau of Longitude, Paris (translated into English by Miss
F. E. Harpham of the Astronomical Department of Columbia University, and
published in the School of Mines Quarterly, vol. xxiii. No. 1, November, 1901.
First and foremost, however, is the classical work of Mechain and Delambre,
Base da SystSme Me'trique, 3 vols. (Paris, 1806-1810), which is the primary
source of information for the early work in establishing the Metric System. It
is, of course, unnecessary to say that in the following pages these works have
been most freely used, and can be recommended for those desiring additional
information on the subject.
42 EVOLUTION OF WEIGHTS AND MEASURES
high degree of precision. Obviously such standards as barley-
corns and human feet did not possess the slightest claim to
invariability, and as soon as the subject began to be considered
seriously and earnestly by scientific men, the choice for the
fundamental unit of linear distance became narrowed to two
classes of lengths, and around them most of the subsequent
discussion centred. One was the length of a fraction of a great *
circle of the earth, while the other was the length or a fraction
of the length of a pendulum, vibrating in intervals of one second
or some other chosen unit of time. For the first, proceeding on
the assumption that the earth was a spheroid (or very nearly so),
it was possible to measure the arc of a great circle even in the
seventeenth century without any great difficulty. Such a measure-
ment involved the determination with considerable accuracy of the
geographical position, or in other words the latitude and longi-
tude, of two points, and then a geodetic 'or trigonometrical '
survey which took into consideration the curvature of the earth's
surface, measuring the actual distance between them in terms of
a unit of length selected for that purpose and represented by a
standard which was employed in the measurement of a base-
line. The distance, as found by the triangulation, could then be
compared with the difference in latitude between the two points,
and thus the actual distance in degrees could be obtained in
terms of the selected linear standard. The other invariable
standard of length was that of a pendulum, which in a given
place executed its vibrations always in the same time. By the /
law of the pendulum, the time of vibration is inversely pro-
portional to the square root of the acceleration due to gravity, and
directly as the square root of the length. Consequently, being
able to measure time, and, assuming that the acceleration of
gravity at a given point is constant, it is possible to determine or
reproduce accurately a given length by this instrumentality.
After considering the invariability of the original standard, the
next important matter to bear in mind is the symmetry and
convenience in actual use of any system of measures which is
based thereon. In the light of the development of the science of
arithmetic and of the popular methods of reckoning, it can be
safely said that the decimal system for money, weights, and
measures, must stand as the most simple and useful. Therefore
DEVELOPMENT OF THE METRIC SYSTEM 43
in considering the genesis of the modern metric system, as a
universal system founded on an invariable standard and sym-
metrically and conveniently developed, it is necessary to go back
to Gabriel Mouton, Vicar of St. Paul's Church, Lyons, who first
proposed in 1670 a comprehensive decimal system having as a basis
the length of an arc of one minute of a great circle of the earth.
One minute of arc would give the length of a milliare or mille,
which would be subdivided decimally into cenhtria, decuria, virga,
virgula, decima, centesima, millesimal The virga and virgida would
be the chief units of the system corresponding to the toise and the
foot then in use. This geometric foot {virgula geometrica) was
further defined by Mouton as corresponding to the length of a
pendulum making 3,959*2 vibrations in a half hour at Lyons.2
This proposition contained essentially the germ of the modern
metric system and Mouton's suggestion of the pendulum was soon
repeated by Picard (1671), and by Huygens3 (1673). The former
said4 " The length of a pendulum beating seconds of mean time
would be called the astronomical radius (Rayon Astronomique), of
which the one-third would be the universal foot : the double of
the astronomical radius would be the universal toise, which would
be at Paris as 881 to 864 If we should find by experience
that the pendulums were of different lengths in different places,
the supposition we had made touching a universal measure
depending on the pendulum would not stand, but it would not
alter the fact that in each place the measure would be perpetual
and invariable."
aSee Bassot, "Historical Sketch of the Foundation of the Metric System,"
Annuaire pour Van 1901, publie par le Bureau des Longitudes, Paris. Translated
in School of Mines Quarterly (New York), vol. iii. No. 1, Nov., 1901.
2 Mouton, Observationes diametrorum Soils et Lunae . . . Huic adjecta est brevis
dissertatio de. . . nova mensurarum geometricarum idea (Lyons, 1670), p. 427. In
reference to Mouton's work an interesting paper by Professor J. H. Gore, "The
Decimal System of Measures of the Seventeenth Century," in the American Journal
of Science (Third Series, vol. xli. Jan., 1891, p. 22), should be consulted.
Professor Gore quotes from Mouton's writings and describes his researches in order
to show that the essential features of the Metric System were first announced by
him. Furthermore he does not consider that due credit was given by the French
scientists who founded the system and made use of Mouton's ideas.
3 Horologium Oscillatorium, 4 prop. 25 (Paris, 1673).
4 Mesure de la Terre, reprinted in Anciens Me'moires, vol. vii. p. 133.
,.\
44 EVOLUTION OF WEIGHTS AND MEASURES
Similar in character to the plan of Mouton, but considerably later
(1720), was a proposition made by Cassini, in his celebrated work,
Be la grandeur et de la figure de la Terre (pp. 158, 159), recom-
mending the adoption of a unit known as the pied geomttrique.
This was equal to ^FOTF Par^ °^ a mmute of arc of a great circle,
and 6 pieds formed a toise. J This foot had a length almost half
that given by the x q o o^) o o o Par^ °^ tne ra(lius of the earth.
Subsequently another plan involving the length of the second's
pendulum as a unit, was brought forward and developed by Du Fay,
and this, after his death, was elaborated and continued by La
Condamine (1747),1 who provided against the variation in length
at various latitudes by taking as his unit the length of the
second's pendulum at the equator (36 inches 7'15 lignes of the toise
of Peru), which he together with Godin and Bouguer had quite
accurately determined at Quito, while engaged in measuring an
arc of meridian at the equator in 1735-1737. La Condamine also
appreciated the advantages of the decimal division of measures of
length, and saw the necessity for reforms in the measures of area,
capacity, weight, etc., so that all might be brought into harmony
with the linear measures, and thus be equally stable and invariable.
He was farsighted enough to suggest, what has since been such a
valuable feature of the metric system, namely the advantages of
international joint effort in making the desired changes, and
advocated consulting with the academies of foreign countries in
this matter.
Worthy of record also is the proposition made by M. Prieur
Du Vernois,2 who urged as the unit of length, that of the second's
pendulum, in preference to that of a fraction of an arc of meridian,
on the ground that the former could be reproduced more readily.
He advocated taking the length of the pendulum at a single point,
suggesting the Eoyal Observatory at Paris, and then making a
standard of platinum, correct at a certain temperature such as 10°,
which would be deposited in the Hotel de Ville. One-third of the
length of this standard would be the French or natural foot,
which would be divided into 10 inches, each inch in turn being
1 Me"moires de VAcademie des Sciences, p. 489, 1747.
2 See Prieur (Du Vernois), Me'moire sur la ne'cessite' et les moyens de rendre
uniformes dans le royaume toutes les mesures d'entendue et de pesanteur, etc. (Paris,
1790), pp. 9-11.
DEVELOPMENT OF THE METRIC SYSTEM 45
s/
divided into 10 lignes. Multiplying the foot by ten would give
the national perch, while an area ten perches square would .be the
national arpent. Units of volume would be measured by cubes of
lignes, inches, and feet, and the unit of mass would be a national
pound corresponding to the mass of a cube of distilled water at
some determined temperature, ten inches square on each edge.
Prieur also advocated a decimal system of money, in which the
lime (franc) was divided into tenth and hundredth parts known
as decimes and centimes.
During the eighteenth century such schemes as have just been
described were proposed by scientists for the improvement of the
weights and measures, and although they were brought to the
attention of the French Government they did not meet with
such approval as to secure their adoption. Indeed there was no
lack of plans proposed by the scientific men, and the government
realized the necessity for uniformity throughout the realm, but
the various schemes were discussed and discarded without any
definitive action, and, just as in later times, the difficulties
attending the introduction of a new system were anticipated
and feared. In fact Necker, in a report made to Louis XVI.
in 1778, speaks of the proposed reform of weights and measures
with considerable diffidence. He writes, " I have occupied
myself in examining the means which might be employed to
render the weights and measures uniform throughout the king-
dom, but I doubt yet whether the unity which would result
would be proportionate to the difficulties of all kinds which this
operation would entail on account of the changing of values
which would necessarily be made in a multitude of contracts, of
yearly payments, of feudal rights and other acts of all kinds. I
have not yet renounced the project, and I have seen with
satisfaction that the Assembly of Haute-Guyenne have taken it
into consideration. It is in effect a kind of amelioration which
can be undertaken partially, and the example of a happy success
in one province would essentially influence opinion."1
With the changes wrought by the Kevolution it was possible
to gain at the hands of the public consideration for radical ideas
in science as well as in government and religion. The .schemes
1 Necker, Compte rendu au Roi de 1778, Bigourdan, Le Syst&me Me'trique,
<Paris, 1901), p. 11.
46 EVOLUTION OF WEIGHTS AND MEASURES
and discussions already mentioned paved the way for the favour-
able reception of a plan for reform when it was urged in the
National Assembly by a bold and able leader. Such was
Talleyrand, then Bishop of Autun, who brought the matter to
the attention of the National Assembly in April, 1790. He not
only appreciated the necessity for a uniform system of weights
and measures for France, but also the desirability of a system
that would be truly international rather than merely the weights
and measures of Paris. He proposed as a fundamental unit the
length of a pendulum beating seconds at 45° latitude, and as a
unit of weight that of a cube of water whose height should be
one twelfth the length of the pendulum. New and most careful
measurements were to be undertaken to determine the length of
the pendulum, and for this purpose a joint commission of the
Paris Academy of Sciences and the Eoyal Society of London was
to be established. Talleyrand's proposal, after being considered
by the Committee on Agriculture and Commerce and discussed
in a report by the Marquis de Bonnay, was brought before the
National Assembly, where, in the course of the general discussion
upon it, the advantages of a decimal division were urged. The
report was accepted and a decree was rendered on May 8, 1790,
which was sanctioned by Louis XVI. on August 22 of the same
year. Inasmuch as this decree describes with some detail the
existing condition and the method of making the change, it is
given below in full. It runs :
" The National Assembly, desiring that all France shall forever
enjoy all the advantages which will result from uniformity in
weights and measures, and wishing that the relation of the old
measures to the new should be clearly determined and easily
understood, decreed that His Majesty shall be asked to give
orders to the administrators of the different departments of the
kingdom, to the end that they procure and cause to be remitted
to each of the municipalities comprised in each department and
that they send to Paris to be remitted to the Secretary of the
Academy of Sciences a perfectly exact model of the different
weights and elementary measures which are in usage.
" It is decreed further that the King shall also beg His
Majesty of Britain to request the English Parliament to concur
with the National Assembly in the determination of a natural
DEVELOPMENT OF THE METRIC SYSTEM 47
unit of measures and weights ; and in consequence, under the
auspices of the two nations, the Commissioners of the Academy
of Sciences of Paris shall unite with an equal number of members
chosen by the Eoyal Society of London, in a place which shall
be respectively decided as most convenient, to determine at the
latitude of 45°, or any other latitude which may be preferred,
the length of the pendulum, and to deduce an invariable standard
for all the measures and all the weights ; and that after this
operation is made with all the necessary solemnity, His Majesty
will be asked to charge the Academy of Sciences to fix with
precision for each royal municipality the relation of the old
weights and measures to the new standard, and to compose
afterward for the use of the municipalities the usual books and
elementary treatises which will indicate with clearness all these
propositions.
" It is decreed further that these elementary books shall be
sent at the same time to all the municipalities to be distributed :
at the same time there shall be sent to each of the municipalities
a certain number of new weights and measures which they shall
distribute gratuitously to those who would be caused great
expense by this change ; and finally, six months only after the
distribution, the old measures shall be abolished and replaced
by the new.
" The National Assembly decrees that the Academy, after con-
sultation with the officers of the Mint, shall offer their opinion
as to the suitability of fixing invariably the inscription of the
coined metal to the end that the kinds shall never be altered
except in their weight, and whether it would not be useful that
the difference tolerated in the coins under the name of remedy
be always beyond requirement, that is to say one piece may
exceed the weight prescribed by law but must never be
inferior.
"Finally, the Academy shall indicate the scale of division
which it believes most convenient for all weights, measures
and coins."
Under the terms of this decree the Academy took up its work
in earnest, and on October 27, 1790, its committee consisting of
Borda, Lagrange, Laplace, Tillet, and Condorcet, made a report in
which they urged the adoption of the decimal division of the
48 EVOLUTION OF WEIGHTS AND MEASURES
moneys, weights, and measures. This report dealt with the
comparative merits of the decimal and duodecimal system of
calculation, and discussed many of the questions bearing on this
subject which have been argued at such length before and since.
Next in importance after settling on the principle of decimal
division was the selection of a unit of length, and a committee
consisting of Borda, Lagrange, Laplace, Monge, and Condorcet,
presented a report to the Academy on March 19, 1791, in which
they stated that, in their opinion, the units suitable for adoption
as the basis of a uniform and rational system of weights and
measures were three in number, as follows : the length of a
second's pendulum, the quadrant of a great circle of the equator,
and the quadrant of a great circle of meridian. Considering the
relative advantages and drawbacks of each of these with great
care and deliberation, the committee concluded that while the
length of the second's pendulum was easily determined and
susceptible of verification, it was dependent on the acceleration '
due to gravity, and that it was necessary to have the position
specified exactly. The most desirable point would be at 45°
latitude, a mean distance between the equator and the pole. At
the latter points, owing to flattening of the earth at the poles,
pendulums vibrating with the same period would have unequal
lengths, that at the equator being shorter as the force of gravity
there owing to the greater radius of the earth is less intense.
But with the pendulum a new and unlike element, namely the
second, is introduced, and this depends upon the arbitrary
division of the day. The preference of the committee was for a
terrestrial arc, inasmuch as it bore a nearer relation to the
ordinary method of measuring distances, and their choice was in
favor of an arc of a meridian rather than one of the equator.
This decision was due to the fact that such an arc could be
measured with greater facility, and also in several countries,
while in addition no more assurance of the regularity of the
equator than that of a meridian could be given.
After an arc had been measured the length of a quadrant
could then be computed, and one ten-millionth of its length could
be taken as the base or fundamental unit of length. In other
words the quadrant was to be measured in a single unit of length
on a decimal basis, instead of in the former degrees, minutes, and
DEVELOPMENT OF THE METRIC SYSTEM 49
seconds. The plan proposed by the committee was to measure
an arc of meridian between Dunkirk, on the northern coast of
France, and Barcelona on the Mediterranean Sea, largely because
these two places were each situated at the sea-level in the same
medidian, because they afforded a suitable intervening distance of
about 9° 30', the greatest in Europe available for a meridian
measurement, because the country so traversed had in part been
surveyed trigonometrically previously by Lacaille and Cassini in
1739-1740, and furthermore because such an arc extended on
both sides of latitude 45°. The committee outlined six distinct
operations essential for the work. They were as follows :
1. The determination of the difference in latitude between
Dunkirk and Barcelona.
2. The measurement of the old bases.
3. The verification and measurement of the series of triangles
used in a previous survey, and extending the same to Barcelona.
4. The observation of the pendulum at 45° latitude.
5. Verification of the weight in vacuum of a given volume of
distilled water at the temperature of melting ice.
6. Comparison of the old and new measures, and the con-
struction of scales and tables of equalization.
The National Academy straightway adopted the recommenda-
tions of the committee, adopting the length of one fourth of a
terrestrial meridian as the basis for the measures of length, and
providing for the measurement of the arc from Dunkirk to
Barcelona, and the appointment of supervisory committees by the
Academy of Sciences. This latter body then addressed itself to
the consideration of a suitable nomenclature, and fixed the length
of the new unit provisionally at 36 inches 11*44 lignes, and
assigning the name Metre to the one ten-millionth part of the
quadrant of the earth's meridian.1 The relations between the
measures of length and capacity, capacity and weight, and weight
and money were also considered. The provisional meter was
derived from a calculation of the observations made by Lacaille
when measuring a meridian in France in 1740. By this the
value of one degree was given as 57,027 toises, which multiplied
by 90 would give the length of the quadrant or distance from
pole to equator, as 5,132,430 toises. Taking the ten-millionth
1 Report of May 29, 1793.
D
50 EVOLUTION OF WEIGHTS AND MEASURES
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52 EVOLUTION OF WEIGHTS AND MEASURES
part of this value, and reducing it to the feet and lignes into
which the toise was divided, the length of 3 feet 11*44 lignes
was obtained. To show how little this provisional meter varied
from the meter finally determined by the commission in 1799, it
may be stated that the latter length in the same units is 3 feet
11*296 lignes, or a difference of about *33 millimeters, an amount
considered quite insignificant in every-day dealings. A standard
of the provisional meter in brass was duly constructed by Lenoir
in Paris, and is preserved in the Conservatoire des Arts et
Metiers at Paris.1
The committee was unable to decide definitely on a system of
nomenclature, and accordingly proposed two schemes : one, as
they termed it, methodical, in which Latin prefixes were used for
the various units ; the other simple monosyllabic names which
they believed would be more readily adopted by the general
population. The Convention, which in the meanwhile had
replaced the National Assembly, adopted the recommendations
of the committee, but preferred to use the methodical nomen-
clature. This decree was dated August 1, 1793, and called atten-
tion to the importance of the steps being taken to secure
uniformity of weights and measures in France, and outlined
the methods of practically establishing the new system through-
out the country. The suppression of the Academy of Sciences
occurred a few days (August 8, 1793) after passing this decree,
and this event, together with various legislative enactments from
time to time, had the effect of causing changes in the personnel
of the scientific staff entrusted with the development of the
system and some differences in the method of procedure. The
place of the Academy was taken by a newly constituted National
Institute of Sciences and Arts, which continued the scientific
oversight, and in general the undertaking was pushed forward as
rapidly as is possible with work of such character.
As showing the extent to which the desire for changes and
reforms was being manifested in France at this time, it may not
be inappropriate to refer at this point to the innovations intro-
duced in the calendar whereby the decimal system was here
applied also. By a decree of November 24, 1793, time was to be
^igourdan, Le Systeme Mttrique (Paris, 1901), chap. ix. pp. 90-93. Mechain
and Delambre, Base du Systeme MUrique (Paris, 1806-1810), vol. iii. pp. 673-690.
DEVELOPMENT OF THE METRIC SYSTEM 53
reckoned from the establishment of the French Eepublic, Sep-
tember 22, 1792, the day of the autumnal equinox. The year as
formerly was to be divided into twelve months, but each of these
was to be divided into three weeks, or decads, of ten days each.
Each day was to be divided into ten hours, and each hour into
one hundred minutes of one hundred seconds each. A picturesque
feature was the grouping of the months according to the seasons
with a different termination for the names of each season. Thus,
beginning with the autumn equinox, Vende'miaire was the month
of vintage, and was followed by Brumaire, the month of fogs, and
Frimaire, the month of incipient cold. At the winter solstice
came Mvose, the month of snow, and then Pluviose, the month of
rain, and Ventose, the month of wind. The spring months were,
Germinal, the month of buds ; Floreal, the month of blossoms ;
and Prairial, the month of flowering fields. In the summer came
Messidor, the month of harvests ; Thermidor, the month of heat ;
and Fructidor, the month of fruits.
This changed calendar was used until 1806, when the Gregorian
calendar was resumed, but the division of the day into 100,000
parts was abandoned in 1795. The lack of success of this method
of dividing time can readily be explained, and by reasons which
have but little bearing on the science of metrology. The doing
away with the Christian Sabbath, the addition of a festival season,
the changing of well-established modes of life by legislative enact-
ment could hardly but be expected to fail of adoption. Further-
more, the Gregorian calendar was at this time practically universal,
and furnished no inconvenience either to scientific men or to the
general public. It was a case of change merely for the sake of
innovation, and as such was destined to fail.
The time being ripe for further and more definite legislation
on the subject of the new scheme of weights and measures, after
Prieur (de la Cote d'Or) had made a full and comprehensive
report describing the status of the work of establishment and
recommending a new system of nomenclature, the Convention
enacted the Law of 18 Germinal an III. (April 7, 1795), which
defined precisely the different units, provided for standards, and
the proper distribution of secondary standards, and the exact
determination of the units of length and mass according to the
original plan. Article 5 of this decree is worth quoting in full,.
54 EVOLUTION OF WEIGHTS AND MEASURES
as it gives precise definitions of the elementary units of the
metric system. It reads :
" Art. 5. — The new measures will be distinguished by the name
of measures of the Eepublic : their nomenclature is definitely
adopted as follows :
" Meter, the measure of length equal to the ten-millionth part
of a terrestrial meridian contained between the north pole and
the equator.
" Are, the measure of area for land equal to a square ten
meters on each side.
" Stere, the measure designed especially for fire- wood, and which
shall be equal to a meter cube.
"Liter, the measure of capacity both for liquids and dry
materials, whose extent will be that of a cube of one-tenth of a
meter.
" Gramme, the absolute weight of a volume of pure water equal
to a cube of one-hundredth part of a meter, and at the tempera-
ture of melting ice.
" Finally the unit of coinage shall take the name of franc to
replace the livre used until to-day."
Greek prefixes were provided to denote the multiples of the
various units and the Latin prefixes for the subdivisions, while in
the measures of weight and capacity, provision was made in addi-
tion for double and half measures.
Under the provision of this law, the scientific work was taken
up with vigor, and the Government appointed a commission of
twelve to complete the original determinations of length and
mass. This body included Berthollet, Borda, Brisson, Coulomb,
Delambre, Haiiy, Lagrange, Laplace, Mechain, Monge, Prony, and
Vandermonde, all of whom had been interested actively in the
work previously accomplished. This commission was then sub-
divided, Delambre and Mechain taking charge of the astronomical
and geodetic work, Borda, Haiiy, and Prony of the determination
of the units of weight, Borda and Brisson of the construction and
verification of the provisional meter, and Berthollet, Monge and
Vandermonde of the construction of the definite meter. The
length of a second's pendulum had already been determined by
Cassini and Borda at Paris, and was found to be equal to 3 feet
8*5593 lignes of the toise of Peru.
DEVELOPMENT OF THE METRIC SYSTEM 55
The measurement of the arc of meridian was the most impor-
tant of the duties of the commission, and involved a vast amount
of labor, both in observations in the field and in the reduction
and calculation of these observations. The work was originally
commenced in 1792 by M^chain and Delambre, and was carried
on by them through various vicissitudes caused by changes in
political conditions, with their consequent effect on the general
and scientific plans for the various operations.
Before describing their work, however, it may be of advantage to
outline the underlying principles of a geodetic or trigonometrical
survey such as is necessary to determine the length of an arc
on the surface of the earth. Such a survey naturally involves
the measurement of considerable distances, taking into considera-
tion the curvature of the earth's surface, and requires a system
or network of triangles connected one with another by means of
common sides. The vertices are stations usually situated on
some high altitude, or at any event so selected that each is
visible with a telescope from several others. Always at one end,
and often at or near both ends, there is what is known as a base-
line, a horizontal distance on level ground actually measured
with a linear standard to as high a degree of precision as is
possible. This involves measuring a distance of from one to ten
kilometers by means of rods, bars, or steel tapes, whose lengths
have been determined with great accuracy at a standard tempera-
ture, to which by correction the actual measurements may be
reduced. Care must be taken to place the standards perfectly
horizontal and end to end when they are being moved over the
measured distance, or to make suitable corrections, and to
observe the temperature. In this way the base line, or one side
of the triangle, marked in the accompanying diagram by a
heavy line, is accurately determined, and it is advantageous
in an extended survey to have the base lines at or near sea-level.
After the base line is determined, then the triangulation may
be reduced and the distance calculated between the remote ends
of the arc. If reference is made to plate vii. vol. i. of the
work 1 of Delambre and Mechain here reproduced, it will be
possible to illustrate the general method. The base shown
between Salces and Vernet is near Perpignan, in the south of
1 Le Base du Systeme Metrique, vol. i.
56 EVOLUTION OF WEIGHTS AND MEASURES
France, and at the end of the old arc previously measured. This
distance is actually measured with the base line apparatus.
Then by means of a divided circle, capable of measuring angles
in both a horizontal and vertical plane, and transit or theodolite
placed at the " terme boreal " (north end of the base line), the
angle between the direction to Mt. d'Espira and to Mt. Forceral
is measured, and then at the " terme austral " the corresponding
similar angles are measured. Thereupon the instrument is taken
to Mt. d'Espira and the angles around that point determined.
This is the beginning of a long series of angle determinations at
all the points of observation, as Mt. de Tauch, Pic de Bugarach,
Mt. Alaric, Carcassonne, etc. All of the measurements are con-
tinually checked by the fact that the sum of all the angles
around a single point, as Mt. Alaric, must equal 360°, and that
the sum of the three angles in any triangle must equal 180°. In
any triangle, if one side and two angles, or two sides and one
angle, are known, then it is a simple1 matter to calculate the
other parts.
In this way it is not only possible to calculate the length of
the sides of all the numerous triangles formed between Barcelona
and Dunkirk, but also the projection of each upon the true north
and south meridian. For example, as soon as the linear distance
from Mt. Alaric to St. Pons is known, and the angle which the
direction makes with the true meridian, then it is simple to
calculate how far one is north of the other, or in other words,
the section of the meridian corresponding to the distance of St.
Pons due north of Mt. Alaric. Thus ultimately the distance of
Dunkirk due north of Barcelona is calculated. The numerous
triangles give continual checks upon the work, as do also other
base lines distributed along the line of triangulation.
The foregoing gives the merest outline of the work of triangu-
lation, as there are numerous refinements and modifications
involved in both observation and computation, which make the
calculation one of no small magnitude. This, however, is but
half of the work. There must be found, with an equal degree of
precision, the geographical position, or, more particularly, the
latitude, of the two extremities of the meridian by astronomical
methods. In kind this is similar to the finding of the position
of a vessel at sea, but more refined methods of observation are
:veO?
e*°
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M Forceral ferme austral
58 EVOLUTION OF WEIGHTS AND MEASURES
necessary, and, at the present day, the nse of the zenith telescope
is considered the most accurate of the several methods of deter-
mining the latitude of a place.
At the time of the measurement of the Dunkirk-Barcelona arc,
however, the astronomers used the method of upper and lower
transits of certain stars near the north pole of the heavens.
Keferring to the accompanying figure, NDBES represents a
DEVELOPMENT OF THE METRIC SYSTEM 59
meridian of longitude through the place, D, the latitude of which
is sought. That is, the plane of the paper is a plane through the
axis of the earth NS and the place D. Evidently then the angle
DCE is the latitude of the place D, and the angle DCN is called
the colatitude. If the line DM indicates the direction in which
& star appears, as seen from D at the instant when it passes the
meridian, then the angle ZDM may be observed, and is called the
zenith distance of the star. The lines DP, DP' and SCN are
parallel, and indicate the direction to the celestial pole, that is,
to the point where the axis NS pierces the heavens, then the
angle ZDP is equal to DON the colatitude of the place. The
angle MDP is the polar distance of the star.
A series of determinations of the zenith distance of Polaris, the
"north star," made on Jan. 17th, 1796, at Dunkirk, for the upper
transit, gave 37° 11' 44"*36. Adding to this the pole distance of
Polaris, lc 46' 39"*60, gives the colatitude 38° 57' 44"*36, and the
latitude, or 90° minus the latitude, 51° 2' 15"*64. In the case of
a lower transit, where the star crosses the meridian below the
pole, the pole distance would be subtracted from the zenith
distance. That is to say, Z'D'P' = Z'DM' - M'DP'. A similar
determination at Barcelona, made on Dec. 17th, 1793, gave as
the latitude of that place, 41° 22' 47"*83. This would give as
the difference of latitude between Dunkirk and Barcelona,
9° 39' 27"*81.
A final determination of the difference of latitude between
Dunkirk and Montjouy (Barcelona) 9°*67380, and the distance,
measured in toises, was found to be 551 584*72. If the refine-
ments of the polar flattening of the earth, etc., are neglected for
the moment, then 551 58472 divided by 9*67380 would give
57 018*7 as the number of toises in one degree of latitude. This
number, 57018*7, multiplied by 90, gives 5 131 680. One ten-
millionth part of this, or 0*5131680 of a toise, would then be the
ideal meter. Naturally, in the actual calculation, all the cor-
rections and refinements were applied.
It must be remembered that in making these measurements
much depends upon the accuracy of graduation of the circles, and
that many measurements must be made and an average taken so
as to obtain in each instance a mean value. The errors can be
•distributed by the two considerations referred to above, that the
60 EVOLUTION OF WEIGHTS AND MEASURES
sum of all the angles around a point must be 360 degrees, and
that the sum of the three interior angles of any triangle must
equal 180 degrees. Furthermore, when the observations are
reduced, allowance must be made for the difference in elevation of
the stations and for the curvature of the earth, which, amounting
to as much as 7 inches for each mile, becomes an important
quantity in an extended survey. Triangulations analogous to
those here indicated, carried out over the whole surface of a
country, are the basis of all accurate map making, and, in. the
United States, an arc of longitude has been measured which
extends across the continent.
The task of measuring the French meridian was divided by
Delambre and Mechain, the former being assigned the northern
portion between Dunkirk and Eodez, a distance of 380,000 toises,
while to Mechain was given from Eodez to Barcelona, a distance
of 170,000 toises. The reason for this unequal division was that
the northern part of the meridian was situated in a much more
accessible country, while Mechain's portion was in the moun-
tainous region of Spain. In addition, the northern part had
been measured twice previously, and the stations had been
selected and recorded. On June 10, 1792, the King issued a
proclamation, in which Delambre and Mechain were commended
to the good offices of government officials and citizens generally,
and various rights and privileges were secured to them. Both
scientists straightway proceeded to their duties, but, owing to the
turbulent conditions in the country, due to the Eevolution, they
encountered from the beginning constant embarrassment and
difficulties. In addition to being arrested and deprived of
ordinary facilities to carry on their work, they met with little
sympathy and co-operation on the part of officials and people, and
experienced great difficulty in erecting and maintaining their
signals, which were oftentimes believed to have been built for
purposes of military communication.
Mechain in Spain had a certain amount of assistance from the
government of that country, but here, as in southern France, he
was harassed and interfered with by political troubles. In fact,
these two resolute engineers experienced almost incredible
difficulties, being arrested by the various governing bodies that
were at that time successively administering the affairs of France,
DEVELOPMENT OF THE METRIC SYSTEM 61
deprived of liberty and freedom, prevented from working by
accident and disease, and, in short, accomplishing most creditable
results under remarkably adverse circumstances.
Finally, in November, 1798, Mechain and Delambre, having
completed their work, arrived at Paris with a record of their
observations, and an international commission invited by the
Directory proceeded to examine and approve the geodetic and
other scientific work accomplished in laying the foundation for
the metric system. This commission consisted of delegates from
the Batavian Eepublic, the Cis-Alpine Eepublic, Denmark, Spain,
Switzerland, the Ligurian Eepublic, Sardinia (later from the pro-
visional government of Piedmont), the Eoman Eepublic, and the
Tuscan Eepublic, in addition to a French Committee composed of
the physicists and mathematicians who had been chiefly concerned
with the development of the system. The commission divided
itself into three sections, each of which carried on a most
thorough examination of the work already done, and made
further calculations and verifications to establish its accuracy and
reliability.1
The first section made a comparison of the bar used in measur-
ing the length of the two bases at Melun and Perpignan, and
found that it corresponded exactly with the toise of Peru.
Examining the toise of Mairan, constructed from the length of
the pendulum beating seconds at Paris, it was found to be "03413
line shorter than the toise of Peru. The second section studied
the measurement of the arc of meridian and the actual length of
the meter, measuring the bases, examining the angles of each
triangle, and finally computing separately their dimensions, em-
ploying different tables of logarithms. The report which was
prepared by Van Swinden, the delegate of the Batavian Eepublic,
one of the committee to whom was assigned the actual calcula-
tion, shows how carefully the work had been done, for, employing
the base at Melun as a starting point in computing the triangles,
it was found that the difference between the computed and
measured lengths of the base at Perpignan was '160 toise (12'28
inches = 31 '19 cm.). When it is remembered that the length of
the Perpignan base was 6006'25 toises, and that of Melun 6075*9
1 For a full account of this work reference should be made to Mechain and
Delambre, Base du Systeme Metrique (Paris, 1806-1810), vol. iii.
62 EVOLUTION OF WEIGHTS AND MEASURES
toises, and that they were 550,000 toises apart, the accuracy of
the measurement may be appreciated.
The flattening of the earth was also computed, employing the
present measurements in connection with those made in Peru,
and it was found to be 3-J-4.1 The most important result was
the calculation of the length of the quadrant of the earth's
meridian, 5,130,740 toises, which straightway gave 3 feet 11*296 *'
lignes as the true length of the meter instead of 3 feet 11*442.
lignes, the length of the provisional meter provided by the law of
August 1, 1793.
The third section, for which Tralles, the Swiss scientist, pre-
pared the report, considered the determination of the unit of
weight and the construction of the standard kilogram which had
been prepared by Lefevre-Gineau, according to plans made by
Lavoisier and Hauy, who performed the first experiments for
this determination.2 The preparation of this standard required
much elaborate experimental work, and it was finally ascertained
that the weight of a cubic decimeter of distilled water at its
temperature of maximum density and weighed in vacuo, was
* 18,827*15 grains, the mean of the sum of the weights of Charle-
magne, which had been employed as the French standard for
over 500 years. While it is not possible here actually to describe
this determination of the unit of weight, nevertheless it is inter-
esting to record that Lefevre-Gineau and his assistant Fabbroni
* discovered that the maximum density of water was reached at
4° Centigrade.
From the sectional reports just mentioned, a general report
was compiled by Van Swinden and presented to the Institute.3
The actual meter standards were then constructed by Lenoir and
carefully compared with the toise standards. A platinum meter
was adopted as the true meter, and was deposited in the Archives
of State, whence it was subsequently known as the Meter of the
Archives. Two other platinum standards4 were constructed at the
1The accepted value to-day is x — , Clarke's Spheroid, 1866.
r J 294-9784 r
2 See Dumas, Lavoisier's Works, vol. v.
3 See Mechain and Delambre, Base du Systeme Metrique, vol. iii. p. 592.
4 See C. Wolf, "Recherches historiques sur les etalons de poids et mesures de
l'Observatoire," Ann. de V Observatoire, Mem. xvii. p. 52, 1883 ; also Ann. de
Chim. et Phys., 5 s. vol. xxv. p. 5, 1882.
DEVELOPMENT OF THE METRIC SYSTEM 6a
same time, and are now known as the Meters of the Conservatory
and Observatory respectively. Iron standards were constructed
also, and were distributed among the delegates. There was also
constructed at the same time a platinum kilogram, and these
standards (kilogram and meter) were formally presented by a
delegation of the Institute to the Corps Legislatif on June 22,
1799, and after being duly received were deposited in the
Archives of the Eepublic. On December 10 of the same year
by statute the provisional meter was abolished, and the new
meter and kilogram definitely fixed and defined, and the stan-
dards presented by the Institute to the Eepublic were adopted as
the definite standards of weight and length.
This act was known as the law of the 19 Frimaire, year VIIL,
and is as follows.1 " Article first. — The provisional determination
of the length of the meter at 3 pieds, 11 '44 lignes, ordained by
the laws of Aug. 1st, 1793, and the 18th Germinal, year III.
(April 7, 1795), stands revoked and void. The said length, form-
ing the ten-millionth part of the arc of the terrestrial meridian,
comprised between the North Pole and the Equator, is definitely
fixed, in its relation with the old measures, at 3 pieds, 11*296
lignes.
"Article second. — The meter and the kilogram in platinum,
transmitted the four Messidor last, to the Corps Legislatif, by
the National Institute of Sciences and Arts, are the definite
standards of the measures of length and of weight throughout the
Eepublic. Some exact copies of the same will be put in the
hands of the Consular Commission, in order to serve as models
for the construction of new measures and new weights.2
" Article third. — The other dispositions of the law of the 18
Germinal, year III., concerning all that is relative to the Metric
System, as well as to the nomenclature and the construction of
the new weights and the new measures, will continue to be
observed."
Provision was made (Article IV.) for a commemorative medal,
which, however, was never made officially, and not actually until
^igourdan, Le Systeme Metrique, (Paris, 1901), pp. 176-177.
2 This article was repealed in the law of July 11, 1903, by which the inter-
national meter and kilogram were officially recognized, and the French copies
(meter 8 and kilogram 35) were made the national standards.
64 EVOLUTION OF WEIGHTS AND MEASURES
1837, when the ideas of the Institute in regard to such a medal
were carried out by MM. Gonon and Penin.
With the scientific determination of the units and the con-
struction of the standards accomplished, there remained but to
effect the general adoption of the new weights and measures.
Several conditions tended to delay this, and at times there was
even pronounced opposition. Chief, perhaps, was the change in
political conditions occurring in France, and it was but natural
to expect on the part of an imperial government little interest in
reforms effected during the republican regime. Furthermore,
there was criticism of the system on account of the lack of
uniformity and organization, as shown by contradictory legislation,
and also on account of its nomenclature, much opposition being
manifested to the use of Greek prefixes. The chief difficulty,
however, was the lack of secondary standards, which were to
have been constructed and distributed at the expense of the State.
Accordingly, it was necessary to repeal such legislation, as the
expense involved was much greater than the government could
afford. Moreover, the temporary office or agency of weights and
measures had been abolished too early to give the much-needed
assistance in accustoming the people to the use of the new
system. There was also embarrassment, due to the fact that,
previous to March 15, 1790, there had been public scales where
the people could weigh their merchandise. These institutions,
which had been done away with by law, it became necessary to
re-establish, and this was done for cities of over 5000 inhabitants
by the Act of 27 Brumaire, year VII. (November 17, 1798), and
subsequently for such other cities as was necessary.
In the meantime, there were not only officials for weighing
and measuring, but also private individuals who carried on a
similar business, and were ready to employ the old as well as the
new and legal measures. As a result, serious abuses and frauds
prevailed, and the general appreciation of the merits of the new
system was decidedly lukewarm. Nevertheless, it made progress,
and was early adopted for all scientific works and papers
published by the Institute to the exclusion of all other systems.
The growth, however, was not as much among the citizens at
large as among the government officials and scientific men. The
reasons given were chiefly that both names and values were
DEVELOPMENT OF THE METRIC SYSTEM 65
changed, that foreign names and words were employed, that the
names were too long, and that the old weights and measures were
persistently used in bills and accounts. To answer these
objections, but with the result of complicating matters further, a
decree was issued 13 Brumaire, year IX. (November 4, 1800),
which stated that the decimal system of weights and measures
would definitely be put into execution for the entire republic
beginning 1 Vend£miaire, year X., and, in order to facilitate its
use, the names given to weights and measures in public documents,
.as in customary usage, should be explained by French names as
given in a list, which to a certain extent corresponded to the simple
nomenclature tentatively submitted by the committee of the
Academy of Sciences in 1793. There was to be no synonym for
the meter, and every measure to which a public denomination
was assigned must be a decimal multiple or subdivision of that
unit. For the measurement of cloth the meter, with its tenth
and hundredth divisions, was to be employed, while the term
Mere was to be used still as a measure of firewood and as a
solid measure, a tenth part of this measure being adopted for
carpentry and known as a solive. The decree also provided that
the new names should be inscribed on the weights already
constructed, and that either one system or the other must be
employed.
While this action tended to weaken the integrity of the metric
system, yet it preserved its fundamental feature of decimal
division, but it was followed by a decree of Napoleon of February
12, 1812, which had a most serious effect on the work already
accomplished, and threatened its very existence. Despite the
objections of Laplace and other scientists, a system of measures
termed " usuelle " was established in which the metric system was
•employed as the basis, but which made use of such multiples and
fractions as would bring about measures that would harmonize
with those long established by the usage of commerce and of the
people generally. The space of ten years was fixed for a period
during which actual experience might occasion further needs of
further changes in weights and measures. The legal or metric
system was to be taught in all the schools, including the primary
schools, and was to be employed in all official transactions,
markets, etc. To carry out the provisious of this decree an
E
66 EVOLUTION OF WEIGHTS AND MEASURES
elaborate series of rules were published by Montalivet, Minister
of the Interior, March 28, 1812.
The " usuelle" measures were all denned in terms of the
metric system, and there were included a large number corre-
sponding to those in daily use. Thus the toise was the length of
two meters, and was divided into six feet, each of which was
denned as one-third of a meter. The foot, in turn, was divided
into 12 inches, and each inch into 12 lignes. For the measure-
ment of cloth and fabrics there was an aune, equal to 12 deci-
meters, divided into halves, quarters, and sixteenths, and also
into thirds, sixths, and twelfths. These divisions for toise and
aune were to be marked along one face of the scale or measure,
while the other must have the regular metric divisions on
the decimal basis. Various weights and measures for retail
business were provided and denned, in which the subdivision was
by halves or some other non- decimal factor not always the same*
Thus, for the measure of capacity, such as grain, there was the
boisseau, defined as ^ of a hectoliter, with a double, half, and
quarter boisseau. The liter also was divided into halves, quarters,,
and eighths, and the shape and material of measures for various
liquids was specified. The lime or pound was defined as equal
to 500 grams or a half kilogram, and was divided into 16 ounces
of 8 gros each. Provision was made for the verification and
sealing of weights and measures by a government bureau, and
also for the construction and distribution of secondary standards
to the various departments.
The use of measures other than the legal ones and those
specified in the decree was forbidden as contrary to law. The
legal system was still to be employed in all government works,
officially and in commerce, and it was explained that the decree
was designed only to affect retail business and the small trading
of daily life. All formal notices must be expressed in legal
measures rather than in those tolerated, and the legal system
was to be taught in the public schools, including the primary
schools, in its completeness. This law was in force until
1837, and its results were most unsatisfactory, since it simply
added to the confusion by increasing the number of weights,
and measures. As, in any event, it was necessary to wait
until the people at large gradually abandoned the old measures,
DEVELOPMENT OF THE METRIC SYSTEM 67
it served no useful purpose in the transition period to add
new measures that essentially were neither new nor old.
The prejudice of the people was slowly overcome, however,
and the instruction given in the schools gradually had its
effect. From government use and general commerce the use
of the legal system extended slowly among retail dealers and
small consumers.
After an experience of a quarter of a century with the
usuelle measures, it was thought that the time had arrived to use
the metric system exclusively, and an attempt to that end was
made in a bill presented in the House of Deputies, February 28,
1837. The matter was vigorously discussed in the chamber, and
was considered by several committees, by whom a plan for
suitable legislation was proposed. Attention was called to the
survival of the old measures and their general use, and to the
fact that the mesures usuelles, while they had contributed much
to increasing the use of the metric system, nevertheless, being
founded on the measures of Paris, were not particularly useful
where these measures had not been previously employed, as
was the case in certain parts of the realm. A general
discussion of nomenclature, systems of division, etc., took place,
but the advocates of the metric system were most earnest in
resisting any modifications, and it was argued that the yield-
ing to prejudice manifested in the legislation of 1812 had
been a serious mistake. It was also urged that people forced
to employ the new system, in order to sell their goods, would
soon learn, and that no new measures should be constructed
whose contents were not in exact accord with the metric system.
Accordingly, after considerable discussion, the following Act was
passed by the Chamber of Peers and the Chamber of Deputies,
and was promulgated July 4, 1837.
Article I. — The decree of February 12, 1812, concerning weights
and measures, is hereby repealed.
Article II. — The use of instruments for weighing and mea-
suring, constructed in accordance with Articles II. and III.
of said decree, shall be permitted until January 1, 1840.
Article III. — After January 1, 1840, all weights and measures,
other than the weights and measures established by the laws of
18 Germinal, year III., and 19 Frimaire, year VIII., constituting
68 EVOLUTION OF WEIGHTS AND MEASURES
the decimal metric system, shall be forbidden, under the penalties
provided by article 470 of the Penal Code.
Article IV. — Those possessing weights and measures, other
than the weights and measures above recognized, in their ware-
houses, shops, workshops, places of business, or in their markets,
fairs, or emporiums, shall be punished in the same manner as
those who use them, according to article 479 of the Penal Code.
Article V. — Beginning at this same date all denominations
of weights and measures other than those given in the table
annexed to the present law, and established by the law of the
18 Germinal, year III., are forbidden in public acts, documents,
and announcements. They are likewise forbidden in acts under
private seal, commercial accounts, and other private legal docu-
ments. Public officers violating this law are subject to a fine
of 20 francs, which shall be collected compulsorily as in a matter
of registration. The fine shall be 10 francs for other violators,
and shall be imposed for every single act or writing under
private signature, but in commercial accounts there shall be only
one fine for every case in which the prohibited terms are used.
Article VI. — Judges and arbitrators are forbidden to render
any judgment or decision in favor of any particular items in
the accounts or writings in which the denominations forbidden
by the preceding article shall have been inserted until the fines
provided by the preceding article shall have been paid.
Article VII. — The inspectors of weights and measures shall
discover violations provided for by the laws and rules concerning
the metric system of weights and measures. They may proceed
to seize weights and instruments whose use has been prohibited
by the said laws and rules. Their testimony in a court of
justice shall be considered as direct proof. The inspectors will
take oath before the tribunal of the arrondissement.
Article VIII. — A royal ordinance shall regulate the manner
in which the inspection of weights and measures shall be
accomplished.
As the metric system gradually became firmly established
in France, the French Government, through diplomatic channels,
called attention of the various nations to its many advantages,
and, at the same time, distributed a number of copies of the
Meter of the Archives, which had been prepared at the Con-
DEVELOPMENT OF THE METRIC SYSTEM 69
servatoire des Arts et Metiers, where now the work of preparing
standards and of carrying on other operations in connection with
the weights and measures took place. For this bureau, a new
comparator, capable of exact measurement and facilitating the
operation of comparison, had been constructed by Gambey, and it
enabled a large number of accurate standards to be prepared for
commercial and industrial use, though in most cases no remark-
able degree of precision was obtained. Important work, however,
was done in the study of platinum standards of the meter for the
Prussian Government, preparatory to the general adoption by
that country, of the metric system. This work was carried
on by Eegnault, Le Verrier, Morin, and Brix.1
With the growing use of the metric system for scientific work,
not only in France, but throughout Europe, the importance of
the accuracy of its fundamental units became a matter of
interest to mathematicians and geodesists in several countries.
Increased activity in geodesy had brought about a number of
measurements of arcs of meridian, and with the resulting data
it became possible to compute anew the shape of the earth
and the length of the quadrant. Any change in this last quantity,
of course, affected the length of the meter as the fundamental
unit of length, and called it into question as an absolute and
natural standard. That such was the case was early demon-
strated by Bessel,2 while General T. F. De Schubert of the
Eussian Army, Colonel George Everest of the British Army, and
Captain A. E. Clarke of the British Ordnance Survey, made
geodetic measurements and studies, which enabled them more
accurately to determine the shape of the earth. As a result of
this work, it was found impossible to depend upon the accuracy
of the determination of the measurement of the quadrant of a
great circle, as it would vary in different places, and required
a most exact knowledge of the shape of the earth.
These questions, it must be remembered, were purely scientific,
and did not influence the practical development of the system
^enolt, "De la Precision dans la Determination des Longueurs en
Metrologie," Rapports Congr&s International de Physique, Tome 1, 1900, p. 45.
2"Ueber einen Fehler in der Berechnung der Franzosischen Gradmessuug und
seinen Einfluss auf die Bestimmung der Figur der Erde." Schum. Ast.
Nachrichten, 1844, vol. xix. No. 438, pp. 98-1160.
70 EVOLUTION OF WEIGHTS AND MEASURES
either in France or abroad, but they provoked much discussion
among scientific men. With the series of world's expositions,
which began with that at London in 1851, an opportunity was
given to the people at large to examine and appreciate the
benefits of an international system of measures, while statistical
and scientific congresses saw the advantages resulting from the
use of uniform weights and measures. Important among these
was a convention formed largely of the official delegates to the
Paris Exposition of 1867, which adopted a series of resolutions in
which the superiority of the metric system of weights and
measures was conceded, the benefits of uniformity stated, and its
adoption by the civilized world urged. Furthermore, the con-
vention deemed it advisable to advocate the study of the metric
system in the public schools, and to recommend its use for
scientific publications, public statistics, postal service, in customs,
and in all works carried on by the governments.
In the same year the International Geodetic Association, com-
posed of delegates from the leading countries of Europe, met at
Berlin, and was engaged in the discussion of topics of great
concern to all interested in scientific measurement. Inasmuch as
many of the standards of length used for base measurements were
all end standards,1 which doubtless had become worn, or possibly
were inexact, these geodesists considered it of the utmost import-
ance that there should be new and common standards as abso-
lutely correct as then existing conditions of metrological science
could make them. This having been done all base measurements
could be referred to the same linear standard, thus insuring that
all European geodetic work could be comparable, and could be
reduced so that a degree of a great circle of the earth could
be determined with accuracy from a number of different measure-
ments. This convention decided that the interests of science in
general, and of geodesy in particular, demanded a uniform decimal
system of weights and measures throughout Europe, and recom-
mended the adoption of the metric system without essential
change, and especially without the metric foot.2 In order to
1 There were by this time a few geodetic line standards, among others those of
Spain, Egypt, and probably that of Clarke.
2Berieht iiber die Verhandlungen der von 30 September bis 7 Octobre, 1867, zu
Berlin abgehaltenen allgemeinen Conferenz der Europaischen Gradmessung, Berlin,
1868, p. 126.
DEVELOPMENT OF THE METRIC SYSTEM 71
secure such a uniformity of measures the convention decided in
favor of the construction of a new European prototype meter
differing in length as little as possible from the Meter of the
Archives at Paris, and compared with it to the highest degree of
accuracy possible. In its construction there would be observed
all refinements secured by the advance of metrological science,
and especially there would be considered its availability for
comparisons with secondary standards of length. The con-
struction of the new standard was to be undertaken by an
international commission appointed by the respective governments,
and the desirability of establishing an international bureau of
weights and measures was expressed. Thus the metric system
came to be recognized as something of international concern, and
its preservation and improvement a matter that concerned the
world at large as well as France.
The action of the Association G-eod6sique was echoed by the
St. Petersburg Academy of Sciences, and this body expressed the
interest of the scientific world at large in a proper standard of
mass, as well as a new standard of length, in a communication to
the Paris Academy of Sciences in 1869, in which they suggested
taking common steps towards the establishment of an inter-
national metric system. This proposition was not enthusiastically
received in France, where many of the scientific men thought
that the meter and the kilogram were the work of French
savants, and looked upon them as something that should not be
tampered with, especially by alien scientists ; but those more
especially interested in metrology perceived that the application
of recent advances in the theory and practice of the science of
weighing and measuring was desirable, and that new standards
•could be constructed with profit, provided that the original
standards should remain as the underlying basis of the system.
Accordingly, on the representation of the Paris Academy of
Sciences, the French Government took up the matter, and after
an examination of the question in its different aspects by a
•committee consisting of representatives from the Academy of
Sciences and the Bureau of Longitude, a report was made in
favor of the proposed plan, and the Minister of Agriculture and
Commerce (Alfred Leroux) brought the matter to the attention
of the Emperor, Napoleon III., in a long and comprehensive
72 EVOLUTION OF WEIGHTS AND MEASURES
statement, dated September 1, 1869, favoring the calling of an
international conference.1
This report was approved by the Emperor, and the French
Government communicated through diplomatic channels with the
various nations, inviting them to send delegates to a conference
to be held at Paris to discuss the construction of a new prototype
meter as well as a number of identical standards for the various
participating nations. This action was especially important as
emphasizing the international character of the system by allowing
the participation of a number of nations in the construction of a
standard that would serve for all, France included. It was also
an admission on the part of the French Government that a new
(line) standard (mMre a trait) was necessary, and that every
means should be taken to conserve the metric system by putting
its standards on a permanent basis.
The invitation was accepted by the nations to which it was
extended, and in August, 1870, delegates from twenty -four States
met at Paris. In the meantime, in order to make suitable
preparations, and to lighten the work of the International Com*
mission as much as possible, the French members had assembled,
and since September 1st, 1869, had been actively engaged in
studying the subject, especially on its scientific side, and preparing
a working basis for the conference.2 Owing to the breaking out
of the war between Germany and France this session was of
short duration, but it was decided that instead of a single new
standard a number of identical standards should be constructed
for the nations participating in the convention, and that one of
the number should be chosen as the international standard, and
should be deposited in some convenient place accessible to all the
participating countries, and under their common care.
Summoned anew by the French Government, the International
Commission met under more peaceful auspices at Paris, on Sep-
tember 24, 1872, thirty States being represented by fifty-one
delegates, among whom were included many distinguished
scientists, and, as was natural, the foremost metrologists of the
world. By reason of the previous session, and the activity of
the French committee in the interval that had elapsed, the
work of the Commission was very clearly mapped out, and
1 Bigourdan, Le Systeme Mitrique (Paris, 1901), pp. 265-272. * Ibid. p. 273.
DEVELOPMENT OF THE METRIC SYSTEM 73
little time was spent in mere preliminary discussion. The first-
and most important announcement was the report of the French
Committee, that after a careful examination had heen made of
the standards of the Archives, the Meter was found in a.
very satisfactory state of preservation, and in such condition
as to inspire all confidence in any operations for which it might
serve as a base. Likewise, the Kilogram of the Archives also-
was found to be perfectly preserved. Comparisons which were
effected between the prototype meter and its contemporaries of
the Conservatory and the Observatory demonstrated that the-
Meter of the Archives had not appreciably altered in length.1
The Commission was divided into eleven committees composed
of delegates specially qualified for the separate branches of the-
work, and the subjects assigned to each committee were as follows:
Study of the ends of the meter of the Archives, material for the-
new meter, its form and method of support, thermometry and
expansion, normal temperature of the meter and kilogram, weights-
in vacuum or in air, comparator, creation of an international bureau
of weights and measures, weight of a cubic decimeter of waterr
material and form of the standard kilogram, balances and
methods of weighing, and preservation of the standards and
providing for their invariability.
Addressing themselves to the consideration of these topics, the
commission speedily reached satisfactory conclusions, and specific-
resolutions were adopted outlining the plans to be followed and
the direct decisions which the Commission had arrived at.2
These resolutions were in substance as follows : The Mttre des-
Archives was to be the point of departure, and was to be repro-
duced by a mMre a traits (line standard), it having been found
that the ends of the platinum bar of the historic meter were
sufficiently well preserved to warrant employing it as an original
standard. This last matter, however, would be finally determined
when the actual work of comparison had commenced. The-
identical copies of the standard meter to be furnished to each of
1 Bigourdan, Le Systtme Metrique, p. 274.
2 For complete text of resolutions and discussion, see Bigourdan, Le SysQme
Mdtrique, pages 299-313. A translation of the same will be found pages 52-55,
"Report of the Committee on Coinage, Weights and Measures," of the House of
Representatives, 46th Congress, first Session, Report 14, 1879.
74 EVOLUTION OF WEIGHTS AND MEASURES
the countries were to be metres a traits, but at the same time a
number of end standards {mhtres a bouts) whose equations would
also be determined, would be constructed for such countries as
specially desired them. The new standards were to represent
the length of a meter at 0 degree centigrade, and the material
was to be an alloy of platinum 90 per cent, and iridium 10 per
cent., with a tolerance of 2 per cent, either in excess or defici-
•ency. The measuring bars were to be constructed from a single
ingot produced at one casting and carefully annealed. Their
length in the case of the metres a traits was to be 102 centi-
meters, and their cross section was carefully designed according
to specification by Tresca.1 Detailed instructions were also
.adopted for the determining of the expansion, the marking, and
the calculation of the equations of the different standards. The
.action of the Commission in reference to the kilogram was as
follows (Section xxii.) : " Considering that the simple relation
which was established by the originators of the metric system
.between the unit of weight and the unit of volume is represented
by the actual kilogram in a manner sufficiently exact for the
•ordinary uses of industry and of commerce, and even for most
of the ordinary requirements of science ; considering also that the
exact sciences have not the same need of a simple numerical
relation, but only of a determination of such relation as perfect as
possible ; and considering the difficulties that would arise from a
^change in the actual unit of the metric system, it is decided that
the international kilogram shall be derived from the kilogramme
<des Archives in its actual state." The international kilogram was
to be determined with reference to its weight in a vacuum, and
the material of the standards was to be the same alloy of
platinum-indium as was employed for the standard meters. In
form the international kilograms were to resemble the Kilo-
gram of the Archives, being cylindrical, with height equal to
the diameter, and with the edges slightly rounded. It was also
decided that the determination of the weight of a cubic decimeter
of water should be made by the Commission, and that a new
balance of extreme precision should be constructed and employed.
The method of weighing and determining the volume of the
kilograms was outlined, but it was decided that, as also in the
1See chapter x., p. 254.
DEVELOPMENT OF THE METRIC SYSTEM 75
case of the mUre des Archives, the kilogramme des Archives should
not be placed in a liquid until the end of the operations.
The plan for actually carrying out the work of the Commis-
sion involved the construction of as many identical standard
meters and kilograms as were needed by the countries interested,
all of which should be made and compared by the Commission,
and required that a standard meter and a standard kilogram
should be selected as international prototype standards in terms
of which the equations of all the others should be expressed.
The actual construction of these new standards, the tracing of
the denning lines, and the comparison with the standards of the
Archives, were entrusted to the French section of the Commission,
which was to perform the work with the concurrence and under
the general direction of a permanent committee of twelve mem-
bers duly appointed to have general supervision of the work.
The Commission also advocated the founding of an inter-
national bureau of weights and measures, to be located at Paris,
which would be both international and neutral, and supported by
the common contributions from the nations party to a treaty
creating such an establishment. It was proposed that it should
be under the supervision of the permanent committee of the
International Metric Commission, and should be used for the
comparison and verification of the new metric standards, for
the custody and preservation of the new prototype standards, and
for such other appropriate comparisons of weights and measures
as might come before it in proper course. In accordance with
the suggestions of the Commission, the French Government again
communicated diplomatically with the various governments rela-
tive to the establishment of such a bureau, and the reports of
the various delegates having in the meantime been made, and the
project in all its details thoroughly understood, on May 20, 1875,
a treaty was concluded at Paris, in which the recommendations
of the Commission were put into effect.1 This treaty was duly
signed by accredited representatives of the following countries :
United States, Germany, Austria-Hungary, Belgium, Brazil,2
^ee Bigourdan, Le Systeme M&rique, pp. 328-337. U.S. House Representa-
tives, Committee on Coinage, Weights and Measures, 46th Congress, 1st Session,
Heport No. 14, pp. 43-50.
2 Brazil did not ratify the treaty.
76 EVOLUTION OF WEIGHTS AND MEASURES
Argentine Confederation, Denmark, Spain, France, Italy, Perur
Portugal, Kussia, Sweden and Norway, Switzerland, Turkey, and
Venezuela. Of the countries present at the conferences, Great
Britain and Holland declined to participate in the treaty or to
contribute to the expense of an international establishment for
the metric system. The British Government, in explanation of
this action, stated that they could not recommend to Parliament
any expenditure in connection with the metric system, inasmuch
as it was not legalized in that country, nor could it support a
permanent institution established in a foreign country for its
encouragement. A change of feeling, however, took place in
England, and in September, 1884, Great Britain joined the
Convention. With the treaty were signed at the same time a
series of regulations for the newly created bureau, and a set
of temporary or transient provisions referring to the work already
in hand which had been undertaken by the French section under
the direction of the conference of 1872. *
The treaty provided for the establishment and maintenance,
at the joint charge of the contracting parties, of a scientific
and permanent international bureau of weights and measures, to
be located at or near Paris, in a territory to be kept strictly
neutral. The bureau was to be installed in a special building,
supplied with the necessary instruments and apparatus, and was
to be conducted by an international committee, composed of
fourteen delegates, each from a different country, with a personal
scientific staff of a director with assistants and workmen. The
first duty of the bureau would be the verification of the new
international metric standards then in progress of construction,
but, in addition, it would have such permanent functions as the
custody of the new international metric prototypes, all future
official comparison with those of the national standards, com-
parisons with the metric standards of other units, the stan-
dardizing of geodetic instruments and other standards and scales
of precision, and, in short, to undertake such scientific work
connected with metrology as would be possible with its equip-
ment, and which would supply the greatest benefits to the
supporting nations. The expense of the new establishment was
to be met by contributions from the various signatories to the
convention, on the basis of their respective population, multiplied
DEVELOPMENT OF THE METRIC SYSTEM 77
by the factor 3 for countries where the metric system was
obligatory, by 2 where it was legalized but not obligatory, and by
1 where it was not yet legalized.1
The treaty was ratified by the various contracting governments,
and the international committee from the conference of 1872 was
continued under the presidency of General Ibanez of Spain, and
authorized to begin the preliminary operations. The first
question was to find a suitable location for the laboratories of
the bureau, and this was solved by the offer of the French
Government to turn over, without charge, the Pavilion de Breteuil,
including a tract of land about two and a half hectars in extent,
situated on the bank of the Seine near Sevres, at the entrance
of the Park of St. Cloud.2 This building, which is on a hill,
dates back to the time of Louis XV., and was used by kings
and emperors as a palace and place of resort, especially by
Napoleon I., who, it is said, was at times wont to study here.
The pavilion itself was in bad repair, having been damaged in the
siege of Paris, but the walls were in good condition, and it was
decided to put the building in order to be used for the offices of
the bureau and the residence of the staff, and to construct a new
and special building for the actual scientific work and for the
safe keeping of the international prototypes. The latter obser-
vatoire or laboratory, a one-story building, was completed and
the apparatus installed from 1878, and has been in constant use
ever since. Its equipment has for the most part been specially
provided, and includes, without doubt, the most complete and
accurate instruments of precision in existence. Each of these
merits a complete description, which is of course not possible
in these pages, but some of the essentials of the more im-
portant instruments will be found described in the chapter on
Standards.3
The construction of the new standards involved greater
difficulties than had been anticipated. The French section
had melted an ingot of the platinum-iridium alloy specified by
the conference of 1872, but it was found to contain impurities
1 It has recently (1906) been proposed by the Committee to drop the coefficients.
8 For description see Bigourdan, Le Systeme Me'trique (Paris, 1901), pp. 353-362.
Ouillaume, La Convention du Metre (Paris, 1902), pp. 21-25.
3 See chapter x.
78 EVOLUTION OF WEIGHTS AND MEASURES
in the form of slight admixtures of rhodium, ruthenium, and
iron. This, accordingly, provoked a controversy, which, however,
was settled by obtaining eventually material which satisfied
all the requirements.
From time to time, as occasion demanded,1 the International
Committee held various meetings connected with the maintenance
and operation of the Bureau International, and in 1887 a
resolution was passed denning the unit of mass as follows :
" The mass of the international kilogram is taken as unity for
the international use of weights and measures."2
This definition enabled a more perfect statement of the funda-
mental basis of the metric system to be made, and produced an
increased exactness which was most desirable. In 1889 a second
International Conference was assembled, which passed on the
work of the International Committee, and approved the standards
which were submitted for their examination, together with a
record of all experiments and investigations that had been made
in their preparation. The conference definitely adopted the
international prototypes of the meter and of the kilogram as the
standards of length and mass respectively, and the centigrade
scale of the hydrogen thermometer was adopted for their
definition and determination. The national prototype standards
were also approved, and were distributed by lot to the various
countries contributing to the Bureau, and, finally, a committee
was appointed to deposit the international standards, — meter
and kilogram, — in the safe of the vault of the Observatory
at Breteuil designed for their reception, and this was accom-
plished with the observance of all due formality, — the various
keys of the apartment being distributed to different officers,5
whose joint presence was necessary for any examination of the
standards.
Mention might properly be made of the elaborate scientific
researches carried on at the Bureau, and the valuable memoirs4
1 Formerly every year ; now every two years.
2 Proces-verbaux du Comite" International des Poids et Mesures pour 1887,
p. 88.
, 3The president of the International Committee, the director of the French
Archives, and the director of the Bureau.
4 See Travaux et Me" moires du Bureau International des Poids et Mesures
(Paris, 1881—).
DEVELOPMENT OF THE METRIC SYSTEM 79-
published at frequent intervals in which these are described.
With the determination of the prototype standards for the meter
and the kilogram accomplished, many other problems in metrology,
such as the study of temperature measurements, the determina-
tion of the meter in terms of the wave-length of light, the
construction of standards for electrical measurements, the study
of alloys for standards, especially those used in geodesy, etc.,,
have received attention from the scientific staff, and the work
accomplished has been of marked and permanent value.
CHAPTER III.
DEVELOPMENT OF THE METRIC SYSTEM IN EUROPE.
While an international system of weights and measures was
■contemplated by the French scientists, yet in the formulation of
the metric system comparatively little general interest was
manifested by other nations, and comparatively little aid was
given by their scientific men. We have seen how an international
•commission of scientists examined and approved the determination
of the meter and kilogram, and the important parts played by
Van Swinden and Tralles in this work of verification.1 These
foreign delegates appreciated the advantages of the new system,
as did other men of science, but the times were unpropitious for
innovations which would unsettle and change the ordinary habits
.and customs of the people. Inasmuch as France was at war
with the greater part of Europe during the opening years of the
nineteenth century, the mere mention of the source of reforms in
weights and measures was in many instances an argument against
their adoption. Furthermore, the actual governments themselves
were changing constantly in many parts of Europe, and the
struggle for territory and national existence was of more im-
mediate importance than such minor matters as those concerning
commerce and the domestic life of the people. Indeed, had the
change been attempted generally at this time it would hardly
have met with success ; for, as we have seen in the case of France,
not only was compulsory legislation eventually necessary, but an
1 The names of nine foreign scientists were attached to the documents accom-
panying the standard meter and kilogram when given to the French Government
for deposit in the Archives.
THE METRIC SYSTEM IN EUROPE 81
able and active administration working on some wise and per-
manent plan was required to put it into effect. Consequently,
before any general consideration of adopting the new system
could take place, it was necessary that there should be perman-
ence and stability in the various governments.
As the fixing of weights and measures is manifestly an
attribute of government, so any successful reforms must depend
upon the character and strength of a particular government, and
in order to influence neighboring countries the territory affected
should be comparatively large and the number of its inhabitants
considerable. Consequently the adoption of the metric system,
in a half-hearted way, by a petty kingdom here and a principality
there, likely at any time either to be absorbed by its neighbors, or
to conquer and to rule them, would and did have little influence
on the general ultimate use of the new weights and measures.
This, however, must not be understood as implying that at the
beginning of the nineteenth century there was no need for
reforms either in Europe at large or in particular states.
Mediaeval conditions survived, and the same evils that prevailed
in France were experienced throughout Europe. The same name
was applied to measures whose values varied considerably not
only in different states but even in different cities of the same
state. Lack of uniformity, both in units and standards, was
universal, with the natural result of hindering commerce and of
generally cheating the less intelligent party to any transaction.
True, French conquest had carried with it the metric system, but
it was used merely under compulsion, and so soon as there was a
change in political conditions the old measures were resumed.
Aside from the scientific propaganda, due to the undisputed
pre-eminence of French workers in exact and applied science,
comparatively little could be done towards forcing the issue, and
the adoption of the metric system waited largely on political
circumstances which affected the life and commerce of the people
at large, and which were duly appreciated by statesmen. These
conditions were brought about by the decline of war, and the
resulting opportunity for the people to turn to the pursuits of
farming, commerce, and manufacturing. If a number of states or
cities were brought into closer political relations, forming a larger
state or possibly a confederation, their commercial relations
F
82 EVOLUTION OF WEIGHTS AND MEASURES
naturally developed, and in order to increase the wealth and
resources of the state, both material and military, it was essential
that the government should take such measures as would best
stimulate commerce and manufactures. Accordingly, it was early
recognized that uniformity of weights and measures within the
boundaries of a state not only contributed but was essential to
the welfare of its inhabitants, while, furthermore, its foreign
commerce was increased by having the same weights and
measures as its neighbors. When we join to these considerations
the fact that the separate systems in nearly all cases were
illogical, inconvenient, and lacking in uniformity and facility of
use, we have the explanation of the eventual spread of the metric
system in Europe.
On the return of Tralles from Paris he endeavored to introduce
into Switzerland the metric weights and measures, and on March
4th, 1801, a law was passed adopting these measures ; but, against
his advice, special names were given^ to the various measures.
Likewise, Van Swinden, after his return to Holland from Paris,
attempted to bring about the adoption of the metric weights and
measures in his own country, and in 1802 the Corps Legislatif
decided in part on the new system. Yet so many features were
lacking from their plan, that the completeness and general
availability characteristic of the system were much impaired, to
the great regret of the scientist. No record has been found to
.indicate whether the law was repealed or never came into effect,
but with the invasion of Holland by Napoleon, a decree of
January 11, 1811, referred the weights and measures of that
country to those of the metric system.1
In Milan, in 1803, the meter and the kilogram were adopted as
the basis of a series of measures arranged on a decimal scale, but
new and local names were given to them. Thus the braccio, as
the unit of length, was equivalent to the meter, while the kilogram
was known as a libbra metrica, or metric pound. In Baden, in
1810, a^jfund, equal to one-half of the kilogram, was adopted as the
unit of weight, and was decimally subdivided. The unit of linear
measure was the ruthe, which was equivalent to three meters,
1Bigourdan, Le Systeme M&rique, p. 241. On August 21, 1816, a law was.
enacted establishing the metric system, and later additional Acts were passed
which will be alluded to in the course of a few pages.
THE METRIC SYSTEM IN EUROPE 83
while the dry and liquid measures of capacity were also defined
in terms of the French metric measures. However, subsequent
legislation was required, and by an order dated August 21, 1828, the
new measures were made compulsory with the year 1831. Some-
what similar steps were taken also in Hesse-Darmstadt in 1821,
the pfund and the shoppen being made equal to one-half a kilogram
and one-half a liter respectively, while the fuss, or linear unit, was
one-fourth of the meter, and the elle four-fifths. In Switzerland,
in 1828, it was proposed to adopt a common system of weights and
measures for the various cantons, and in 1835 twelve of these
divisions entered into an agreement known as the " Maass
concordats," to which reference will be made later. This plan
consisted essentially of the usual measures defined in terms of the
metric units.
The French Government, as we have seen, having experienced
difficulty in securing the exclusive use of the metric system by its
own people did not take active measures towards extending its use
abroad until after the passage of the law of 1837, which rendered
the system universal and compulsory throughout France. In 1841
the Minister of Agriculture and Commerce, Cunin-Gridaine, con-
sidered that much good would be accomplished by the exchange
of standards of weights and measures between France and the
important commercial countries of the world. He was supported
by the Minister of Foreign Affairs, Guizot, who arranged for such
an exchange through the diplomatic channels of the various
governments.1 Accordingly these standards were duly sent, and
in 1853 the United States received a complete series of French
standards, which included a steel meter that had been compared
with the platinum standard at the Conservatoire des Arts et
Metiers, and likewise a gilt kilogram whose constants had been
determined in terms of the kilogram of the Archives.
The beginning of a general feeling in favor of the universal
adoption of a single system of weights and measures, and the
opinion that for this purpose the metric system was the most
suitable, may be considered to date from the London Exposition
of 1851, to which reference has already been made. Despite
the fact that metric weights and measures had been used, and
their adoption advocated by scientific workers, it cannot be said
1 Bigourdan, Le Systeme M6trique, p. 245.
84 EVOLUTION OF WEIGHTS AND MEASURES
that before this time the importance of the subject was recognized
generally, and that economists and statesmen had thoroughly
realized the benefits that would ensue from a single and
universal system of weights and measures, as well as a common
and universal basis for coinage, in which there should be a
single, and preferably decimal, principle of division. But from
such a beginning the agitation spread, and nearly every nation
soon had a group of earnest advocates of the metric system,
which included not only such scientific men as chemists,
physicists, astronomers, and engineers, not to mention economists
and statisticians, but also merchants and manufacturers. This
was due to the bringing together from many quarters of the
globe of a large number of representative merchants, producers,
and manufacturers, with their various wares and products, and
also scientific men and others who were called to pass upon the
comparative merits of the various articles on exhibition. At
the conclusion of the London Exposition, the Society of Arts,
in a communication addressed to the Lords of the Treasury, asked
if it were not possible that some arrangement could be made
whereby a universal decimal system of moneys, weights, and
measures could be adopted in common for all the nations of the
world. This was possibly the first expression in England, outside
of scientific circles, of the general advantages of universal weights
and measures, and particularly those that would accrue to com-
merce by the adoption of a uniform decimal system. In 1855
an international statistical congress was held at Paris, and on
the motion of James Yates, a member of the Eoyal Society
of London, it was decided to form an International Association,
to advance the adoption of a decimal system of weights and
measures and moneys. This association made an examination of
the different systems employed throughout the earth, and decided
that the metric system, on account of its scientific character and
general availability for international trade, was to be preferred,
and accordingly made a recommendation in its favor. The
sentiment was further echoed by members of the International
Jury of the Paris Exposition of 1855, who formally adopted
resolutions in favor of the metric system, recommending it to
the attention of their respective governments, and urging its
adoption on the ground that it would not only promote commerce,
THE METRIC SYSTEM IN EUROPE 85
but also peace and unity of feeling throughout the world, praising
especially its decimal basis.1
A Committee of Weights and Measures and of Moneys, com-
posed of delegates of various countries to the Paris Exposition
of 1867, was formed at the initiative of these delegates, and took
action in favor of the decimal system, and urged the adoption
of uniform weights and measures throughout the world. While
this committee enjoyed no official standing, yet it adopted reso-
lutions recommending the study of the metric system in all the
schools, and its recognition in all public meetings. Furthermore,
its exclusive use in scientific and statistical publications, for
postal purposes, in the customs, as well as in public works,
and in all other branches of government administration was
recommended.2
In the meanwhile, the inconvenience and confusion caused by
different weights and measures throughout Central Europe had
reached a point where positive action was necessary. Under
more peaceful conditions, commerce and industry were beginning
to flourish, and the lack of uniformity in weights and measures
was proving a serious hindrance to trade. In a comparatively
small territory there was a considerable number of different
states with different systems of weights and measures, as well as
with different tariff and customs regulations, which seriously
interfered with the easy transaction of international business.
The multiplicity of these measures involved the employment of
an inordinately large number of clerks and computers in custom
houses and counting rooms to change from one system to another
weights, measures, and moneys, as specified in invoices, and other
documents. It was doubtless also realized that to carry on
commerce there must be an easy standard of comparison between
the goods of the home country and those of other foreign coun-
tries. The money alone was recognized as a sufficient cause of
trouble, and extensive reforms, such as the decreeing of uniform
(Metric) weights for metallic currency by the Vienna Coin
Treaty of January 24, 1857, and a similar action by the so-called
Latin Union of 1865, improved materially conditions in this
respect, and it may be remarked that in both instances the
currency was put on a decimal basis.
1 Bigourdan, Le Systeme Mttrique, p. 248. 2 Ibid. p. 248.
86 EVOLUTION OF WEIGHTS AND MEASURES
With the weights and measures, however, the first steps to-
ward uniformity were taken when the metric system was adopted
for customs purposes, some time before its legal adoption for
general use in the separate states. Thus the German Zollverein
(Customs Unions)1 adopted for use in the customs a standard
metric pound {zollpfund) which was one-half of a kilogram, and
with it a centner of 50 kilograms. These units of weight came
into effect January 1, 1854, and the pfund, which was divided
into 30 loth, was adopted by the German- Austrian Zollverein, for
postal purposes, on the same date. In 1856 the use of the metric
pound and centner was further extended, and in 1857 a coin
pound or munzpfund (500 grams) was employed for coinage
purposes. The railways also followed the example set by the
customs, and throughout the countries constituting the Zoll-
verein all freight was weighed by the metric pound. Thus it
will be seen that the entering wedge of the metric system in
Europe outside of France was in the adoption of uniform weights
for international trade, which led to a general knowledge of its
merits and appreciation of the advantages of uniformity.
The natural and immediate result was the adoption of the
" zollpfund " as the unit of weight in a number of states, and with
this came a general understanding of the inconvenience attending
the use of different standards for measures of length, capacity,
etc. In consequence, a commission of scientific men was
appointed from the federated German states to examine the
question thoroughly, and formulate a national system of weights
and measures. They reported in 1861 that the metric system
already possessed the advantages sought after, and that greater
benefits would ensue from its adoption as a whole than by
devising a new system or by endeavoring to harmonize existing
standards.
The method of the change in Germany is well worth careful
study from the student of metrology and of public affairs, inas-
much as here were represented most of the problems which
1 The Zollverein, or union of German states to secure among themselves freedom
of trade and uniformity of duties on foreign imports, was proposed by Prussia in
1818. The North and South German Unions, formed for this purpose, were
united in 1829 by a treaty which became effective in 1834, and in 1854 a strong
union of nearly all the German states was brought about.
THE METRIC SYSTEM IN EUROPE 87
would be encountered were the same change to be made in the
near future either in the United States or in Great Britain. In
fact, the conditions may be said to be practically the same, for
although standards and processes based on Anglo-Saxon measures
have since developed to such an extent that a change would be a
serious matter, yet, at the same time, the use and knowledge of
the metric system have also increased, so that on this score the
change would be far less difficult now than it was for Germany
in 1870. Furthermore, reforms in arbitrary gauges and methods
of measurement are now required in various lines of industry and
manufacturing, which make the present an especially appropriate
•time for a general change in measures. Consequently, by study-
ing methods and conditions in Germany at the time of this
change, it is fair to say that an accurate knowledge of the general
features of any present problems of this description will be gained,
and it is also safe to say that the final advantageous outcome
would be reproduced in either the United States or Great Britain,
though the time necessary to accomplish such a consummation may
reasonably be a subject for difference of opinion and argument.
The first legislative step in the introduction of the metric
system into Germany was the adoption of resolutions to that
effect by the Federal Council and the Parliament of the North
German Confederation, which were published under the date of
August 17, 1868.1 These resolutions provided that the metric
system should be adopted in place of the weights and measures
previously in use, and that the system should be optional on
January 1, 1870, and obligatory on January 1, 1872. No change
in the nature or execution of this plan occurred when in April,
1871, the confederation was superseded by the empire. There
was duly established the " Normal- Aichungs-Kommission," which
was charged with the work of furnishing detailed directions and
specifications as to the material, shape, and other characteristics
of the weights and measures, and also with supplying the
*' marking " office and its various local branches with such imple-
ments as would enable it to mark and stamp all weights and
measures which should be presented to it. It was also ordered
1 W. Foerster (former Chief of the German Bureau of Weights and Measures,
and President of the International Committee of Weights and Measures), pp. 12,
13, House of Representatives, Paport No. 2885, 54th Congress, 2nd Session, 1897.
88 EVOLUTION OF WEIGHTS AND MEASURES
that the confederated governments publish the calculations giving
the figures for the legal equivalents of the new weights and
measures as compared with the old.1 The Commission had charge
of the introduction of the new system throughout the confedera-
tion, supervising all measures to facilitate its speedy acceptance,
and with definitely carrying it into effect. The various states of
the confederation appointed officials for the actual marking and
stamping of the measures and weights, and prescribed regulations
for the administration of such bureaus. In the ten months
previous to the date assigned for the beginning of the optional
use of the metric weights and measures, the Commission provided
all the marking offices with standards for the verification of such
weights and measures as should be presented to them for legaliza-
tion, and immediately after these needs had been met the
manufacturers were provided with proper standards, so that they
could at once commence the manufacture of weights and measures
for general sale and use. Such weights and measures, adequate
in number and of high accuracy, were soon forthcoming, and by
the end of the first half of the year 1870 a large part of the
people of Germany became well acquainted with the new
measures, their decimal division appealing particularly to the
industrial and technical workers.
In 1870 occurred the war with France, and, while it prejudiced
many of the people against the new weights and measures, never-
theless it more closely united Germany and thus offset any
difficulties on this score. In short, on the arrival of the
specified date, January 1, 1872, when the use of the old weights
and measures must cease and the metric system be the only
legal system, not only were the new weights and measures
supplied to all places throughout Germany where merchandise
was sold, but the various tradesmen and others concerned had
actually learned the use of meter sticks, liter measures, and the
series of gram weights. This record is somewhat remarkable,,
as in Germany there was not one system of weights and
measures, but, as has been shown, a large number of different
systems which the new measures had to supplant. Germany,
however, enjoyed one great advantage in the adoption of the
metric system in the extensive use in a number of the
1 Same Report, pp. 7, 8.
THE METRIC SYSTEM IN EUROPE 89-
states of the " zollpfund " or customs pound, above mentioned,
which we have seen was the weight of 500 grams or a half
kilogram. Weights of this denomination were actually in
existence in considerable numbers and were widely employed,
but the subdivisions were not usually on a decimal or metric
basis, and only in one state, Hanover, was there a division into
1000 half grams. Two of these pfund weights immediately
furnished a legal kilogram, and, while their use interfered
somewhat with the development of the decimal principle, never-
theless it served to accustom the people at large to the new
mode of reckoning. The liter measures were accepted even
more readily than those of mass. The relation between the
unit or liter and the measure of length and the weight of water
served to commend the new system readily to those dealing-
with fluids, while a number of simple tables were prepared
officially to explain the simplicity of the system.
In contrast to the ease with which the liter and the gram
series were adopted, mention must be made of the change
in the measures of length. The principal measures of length
were the ell and the foot, which, though varying greatly among
the various German states from a metrological standpoint, were
approximately the same, or sufficiently so at least, to conveys
to the ordinary person a certain rough idea of extension which
for many purposes sufficed. Furthermore, the foot and ell
differed so much from the meter and its subdivisions that the
purchasing public could not transfer readily the price of cloth or
other material when conceived or expressed in these units to the
meter, and thus obtain even an approximate idea of value. It
was also argued that the meter was not as convenient to think
in as the foot for architects and mechanics, by some of whom
opposition to the new measures was manifested ; but this feeling
soon died away, and the new measures were soon universally
employed in all works and calculations.
That the metric system has contributed materially towards the-
upbuilding of German commerce and industry is universally
conceded, but, of course, since its adoption so many causes have
acted to this end, that it is not possible to state precisely just
what part the international measures have played. Suffice it to
say, that in manufacturing, especially of articles where precision
r
90 EVOLUTION OF WEIGHTS AND MEASURES
of measurement, and interchangeability of parts are essential,
the Germans have vastly improved and increased their output,
which must in a certain degree be due to this cause. Inasmuch
as the metric system was employed extensively in scientific
work previous to its general adoption, the increased activity of
German investigators in fields where measuring is essential is
not necessarily a result, but the readiness with which industrial
workers have availed themselves of the scientists' labors has
doubtless been facilitated by the fact that their processes and
results were expressed in a language that readily could be
understood.1
Austria, where there was much the same variation of feet,
pounds, etc., as in Germany, followed that country's example,
and on July 23, 1871, the Parliament passed a law providing
for the permissive use of the metric system after January 1,
1873, and its compulsory use after January 1, 1876. At
the same time it published official tables of equivalents
between the old and new measures, and established a standard
meter, which was an end standard of glass, and a standard
kilogram of rock crystal, these being legally supplanted in
1893 by the copies of the international standard meter and
kilogram received from the International Bureau. The old
measures, especially those known as the " Lower Austrian
System," were quite unlike those of the metric system, and at
first it would appear that there would have been great difficulty
in bringing about a change ; but for a while a binary system
of division was tolerated, and certain weights and measures
approximate in value to the older ones temporarily were
employed. In the meantime newspapers and schools were
zealously educating the people to the new order, while the
government prepared an adequate number of approved weights
and measures, as well as supervised the construction of others
according to standard regulations. The four years appointed
for the transitional period proved ample, and there was no
expressed or obstinate resistance on the part of the people.
In fact, it was the general opinion that any lack of completeness
1See Promemoria of German Imperial " Normal- Aichungs Kommission " in
House of Representatives, Report No. 2885, 54th Congress, 2nd Session, 1897,
pp. 7-9.
THE METRIC SYSTEM IN EUROPE 91
in the adoption of the system was due rather to laxity on the
part of the municipal authorities than to any pronounced feeling
of the public at large.1
In Hungary, by the law of 1874, Article VIII., the metric
system was established to be in force from January 1, 1876, but
its use was sanctioned six months earlier, and finally, in 1901, the
international standards were duly established by law. The
method of making the change was in the main the same as in
Austria, and the new weights and measures were quickly
naturalized and adopted by the people generally, though in
isolated districts the old usage was maintained for many years.
Outside of France, Belgium is one of the earliest countries to
use the metric system, as it was established there by the law of
August 21, 1816, at a time when that country was united with
Holland.2 The names of the old units were applied to the
metric values, but instruction in the metric system was given in
the schools, so that, after the system had been rendered com-
pulsory from 1820, by 1836 it was possible to withdraw the
Belgian names, and in 1855 the exclusive use of the French
1See pp. 9, 10, House of Representatives, Report No. 2885, 54th Congress,
2nd Session, 1897. In addition to this report, which contains information
furnished by European governments to ambassadors and ministers of the United
States on the subject of the adoption of the metric weights and measures by
the different countries, a summary of foreign legislation on the Metric System
prepared by J. K. Upton, chief clerk of the Treasury Department, and later
Assistant Secretary of Treasury, contained in Report No. 14, House of Repre-
sentatives, Committee on Coinage, Weights and Measures, 46th Congress, 1st
Session, 1879, has been drawn upon for dates and details given in the following
pages concerning the adoption of the metric system by the nations of Europe.
Somewhat more recent are the summaries contained in Guillaume, La Convention
du Metre (Paris, 1902), Annexe iv. pp. 218-226; "Resume de quelques Legis-
lations relatives aux Poids et Mesures," Annexe aux Proces-verbaux des Stances
du Comite' international des Poids et Mesures, Session de 1901, 2e Serie, Tome 1
(Paris, 1901) ; Reports from Her Majesty's Representatives in Europe on the Metric
System, part i., July, 1900, English Parliamentary Accounts and Papers, 1900,
vol. xc. ; Reports from Her Majesty's Representatives Abroad, part ii., February,
1901, English Parliamentary Accounts and Papers, 1901, vol. lxxx. The latter
are particularly full, and give an interesting account of the transition period, as
well as the extracts from the laws in many instances. There is also available the
Beizieme Rapport aux gouvernements signatoires de la Convention du Metre and the
Comptes rendus de la deuxieme Conference generate des Poids et Mesures, 1895.
2 See ante, p. 82.
92 EVOLUTION OF WEIGHTS AND MEASURES
names and measures was established by law. The Belgian
standards of mass and length were copied from those in France,
being legalized in 1848, but they were damaged in the fire of
1883 at the Palais du Nation, so that the international prototypes
which were received in 1894, and duly legalized, were most
acceptable.
The use of the metric system in Egypt is of interest, inasmuch
as that country is so largely under British influences, both
commercial and political. The metric system was established on
a permissive basis in 1873, by a decree of Khedive Ismail, which,
however, was not enforced, so that in 1886 a commission was
appointed to consider the adoption of the metric system, and
reported in its favor. By 1892 its use had extended, so that it
was possible for the government to adopt it for use in all trans-
actions between it and private parties, except for measurement of
land and the tonnage of ships. It has been employed in the
public works department, where large engineering projects have
been supervised and executed by British engineers, who have
recognized its many advantages, and also in the customs, post
office, and railways. While the old native measures still remain
in daily use, yet the metric system is being taught in the
government schools, and as rapidly as is possible for an oriental
people, with their traditions and conservatism, it is growing into
increased use.
Greece is an example of a country where the Government
though having adopted the metric system is unable to secure
its use by the masses of the people. The metric system was
established by a royal decree of September 28, 1836, with Greek
names for the different weights and measures; but its use is largely
confined to the Government in its various transactions involving
measures of distance and area, the Government in common with
the general public employing the oke — T282 kilograms as a unit
of weight, and a measure of the same name = 1*33 liters as a,
unit of capacity. This is undoubtedly due to the fact that the
amount of international commerce in Greece is comparatively
limited, and that the people at large have but little interest
in general commerce as such, while the Government is indisposed
to press reforms of this character.
The conquest of Lombardy and Venetia by Napoleon in 1803-
THE METRIC SYSTEM IN EUROPE 93
was the means of inaugurating the metric system in Italy, but
its general use did not follow except in governmental transactions,
and the bulk of the people resisted this effort on the part of
foreign conquerors. In some of the various kingdoms and princi-
palities it was found convenient to adopt the metric weights and
measures,1 but it required the establishment of the Kingdom of
Italy in 1861 to ensure complete uniformity and the thorough
adoption of the system. Here, again, we see that one of the
consequences, or possibly a necessary attribute, of the establish-
ment of a nation from a number of separate states is that there
should be a single and uniform system of weights and measures.
Accordingly, by the law of July 28, 1861, the metric system was
rendered obligatory throughout the kingdom after January 1, 1863,
and this was reinforced by a law passed in June 23, 1874; and
on August 23, 1890, the international standards were established
by a royal decree.
The Japanese have for some time used metric weights in their
coinage, and in 1891 a law was passed in which the ancient
measures were reorganized and based on those of the metric
system, which was also duly recognized. The various national
units, which are divided either decimally2 or sexagesimally, are
defined in terms of the metric units, so that little difficulty
would be experienced in passing from one to the other, and,
in fact, tape measures are frequently graduated on both sides with
the two scales, while on a map both scales are usually given.
We have seen above 3 how the metric system was introduced
into Holland when it formed one country with Belgium in
1816, and it gradually enjoyed wider use until in 1869 the
^French names were adopted to designate the different units,
while permitting the older and national names to be used for
ten years longer. The royal standards of the Netherlands were
constructed by a commission of Dutch scientists, and while they
1 Metric System was made compulsory in Piedmont in 1845 ; introduced into
Modena in 1849, with eight years for its gradual adoption ; adopted in part
of Papal States in 1859 ; in 1861 adopted in Sardinia ; in 1863 adopted in
Neapolitan provinces, in 1869 in Venice, and in 1870 in Rome.
2 Japanese measures below a shaku= -99421 feet = ^ meter are decimally
divided, rendering their comparison with metric measures in the case of
drawings or diagrams very easy.
3 See ante, pp. 82 and 91.
94 EVOLUTION OF WEIGHTS AND MEASURES
resemble those of the International Commission, were derived
directly from the standards of the Archives. The Dutch
standard meter is 2#7 microns longer than the international
standard.
When a decree was issued in Portugal in 1852 providing for
the introduction of the metric system, it was provided that it
should be in full legal operation within a space of ten years. It
was planned that the introduction should be by successive stages,
beginning with the Government, and various schemes and tables
of legal equivalents were to be prepared and distributed. It was
not possible to bring about the change during the specified time,
so that subsequent statutes were necessary, and it was not until
1872 that the metric system was officially in universal use. The
introduction of the new weights and measures was attended with
no difficulty, save the lack of intelligence of the people of the
lower and agricultural classes, and among them the force of
custom and tradition has proved so strong that old weights and
measures still remain, though they cannot be used in any receipt
or legal document. The metric system is, however, greatly
appreciated by the commercial interests, and is slowly but surely
making progress among the people at large. In fact, it will be
seen that among intelligent people such a change occasions
comparatively small inconvenience and is quickly effected ; but
where there is a low general standard of education, as in Portugal,
the people are conservative and unwilling to accept innovations,
as they are unable to appreciate their utility.
Russia, no less than other countries, early felt the necessity for
reforms in its systems of weights and measures, and in 1833 the
original Russian units were denned in terms of English feet, —
the legal unit being the sagdne, which was equal to seven English
feet. The standard for this unit was constructed with great
exactness, and was compared with the English yard, and from it
the various other measures were derived. Nevertheless it was
found necessary to replace the sagdne by the archinne, which is
i sagdne or '71112 meter. The metric system is now permissive
under the terms of the law of June 4-16, 1899, which became
effective January 1, 1900 ; yet it is noteworthy that its inter-
national character is recognized by denning the national stan-
dards, the livre and the archinne, in terms of the international
THE METRIC SYSTEM IN EUROPE 95
prototypes.1 The metric units are largely employed in Russia, as
elsewhere, for scientific work, and there is said to be a strong
feeling towards the complete adoption of the system, which for a
number of years has been used by the pharmacists of the empire,
and since 1896 by the medical departments of the Russian army
and navy. The metric system is also used in the customs ser-
vice, with indications of further extensions. In Finland, where a
higher standard of education prevails, the metric system has been
employed with considerable success since 1892, and no difficulty
attending its introduction was experienced.
Notwithstanding the fact that a large part of the preparatory
work in determining the length of the earth's quadrant had been
done in Spain, that country did not adopt the metric system until
1849, though previously it had been under discussion, and so early
as 1807 a number of metric scales had been constructed at Madrid.
The law of 1849, which provided that the system should go into
force in 1853, and actually became operative throughout the entire
kingdom in 1855, defined the meter in terms of the dimensions of
the earth, and the other units as deduced from the meter. These
definitions remained in force until 1892, when the receipt of the
copies of the international prototype meter and kilogram, prepared
by the Bureau International, necessitated the restatement of the
law in which these standards and their relation to the inter-
national prototypes of the Bureau were duly recognized.
In Sweden a royal decree was issued November 22, 1878, by
which the use of the metric system was made optional from the
following January 1 , and after ten years was to be made compulsory.
The usual official tables and information in various and convenient
forms were distributed during this transition period, but it was not
until the end of the appointed time that the metric system came
to be used generally. After that its employment became prac-
tically universal and no difficulties or opposition were experienced.
In Norway the metric system was employed in the postal
service, by the Act of May 3, 1871, and in the same year the gram
was adopted as the unit of weight by the medical profession of
that kingdom. In 1879, on July 1, the use of the metric system
for all private business became optional, but from this date it was
1 See Proces-verbavx dn Comity international des Poids et Mesures, Session 1897,
p. 155.
96 EVOLUTION OF WEIGHTS AND MEASURES
to be used exclusively by the Government in all its transactions,
such as the collection of customs duties, public accounts, taxes,
etc. Then on July 1, 1882, the use of the metric system was
made obligatory in all transactions, both public and private, and
no other weight, measure, or coinage other than metric was
permitted. It is interesting to note that during the three years
of the transitional period the government altered certain of the
older weights and measures, making them conform to the
metric system. Thus all weights of one pound and over during
the first two years were regulated and made over free of cost, so
that the old Norwegian " skaal-pund " and the old " bismer-pund "
used with the steelyards were slightly increased so as to weigh
half-kilograms. Likewise the old " korn-tonde," or corn measure,
was adjusted to hold 140 liters, and a half measure to hold 70
liters. In the third year of the change period, however, a fee was
required for these alterations, and after the compulsory use of the
new weights and measures they were absolutely prohibited.
In the case of Norway we have an approximate statement1 of
the cost of the introduction of the metric system as given in a
statement of the value of instruments sold in the years 1877-84
by the Weights and Measures Office, but this does not of course
include the private sale of metric weights and measures. In this
€onnection it must be borne in mind that the population of
Norway at this time was somewhat less than 2,000,000.2 The
statement is as follows :
Public expenses —
Purchase of standards, weights and measures
and apparatus ----- £2,844
Plans and drawings- - - - - 217
Models 306
Controlling apparatus for town and country
police - 1,650
Adaptation of old instruments to the metric
equivalents - - - - 3,111
£8,128
1 Reports from Her Majesty's Representatives in Europe on the Metric System,
part i., July, 1900, pp. 63, 64 ; E.P.P., 1900, vol. xc.
2 Dec. 31, 1882, 1,913,000.
THE METRIC SYSTEM IN EUROPE 97
Private expenses-
Adaptation of old instruments to the metric
equivalents - £2,044
Purchase of new metric instruments - - 35,761
Total cost of introduction £45,933
In Switzerland there was even more than the usual diversity of
weights and measures in the different cantons, but after 1822 in
some of these divisions a system based on the metric measures and
having a foot of 30 centimeters and a pound of 500 grams was
established. By an agreement known as the " Maass concordats,"
dated August 17, 1835, twelve cantons united in establishing this
system, and by subsequent additions to the convention and by
legislation it became operative throughout the nation, being by an
Act of Dec. 24, 1851, the national and compulsory system through-
out the confederation after December 31, 1856. In this system
the legal unit of length was the pied or foot, equal to 30 centi-
meters, divided decimally, and having such multiples as the brache,
2 feet ; the mine, 4 feet ; the toise, 6 feet ; the perche, 10 feet ;
and the lieue, 16,000 feet. The livre or pound equal to 500 grams
could be divided either on a binary or a decimal system, while
for dry capacity the unit established was the quarteron, equal
to 15 liters, and for liquid capacity the pot, equal to one and
a half liters. On July 3, 1875, the Federal Chamber passed a
law providing that the complete metric system should be used
after January 1, 1877, and that the standards then in course
of preparation by the International Commission should be the
legal and national standards. These international prototype
standards were received in 1889, and were duly substituted for
the older standards.
In Turkey, metrological, like other reforms, have not
achieved the success deserved, largely on account of the char-
acter of the people and the Government. In 1886 a law was
passed providing for the establishment of the metric weights and
measures in Constantinople, and making their use compulsory
after five years, and in 1891 ancient measures were confiscated
and destroyed ; but it has been recognized as practically impossible
to enforce the system, and old and new units and standards have
nourished side by side. In fact, experience demonstrates the
G
98 EVOLUTIOxN OF WEIGHTS AND MEASURES
strength of the proposition that weights and measures and their
preservation intact and uniform are correlatives of government,
and where the latter is weak or deficient in character, a satis-
factory condition of these necessary adjuncts to commerce cannot
be maintained. Nevertheless, in 1900, it was reported1 that all
scales imported into the Ottoman Empire must be marked in the
metric system, and all weights and measures marked according to
the old systems were liable to confiscation.
In England the need of an international and decimal system of
weights and measures was realized as early2 as 1783 by James
Watt, who had considerable difficulty in reducing the weights
and measures used by Lavoisier and Laplace in some experiment
to the English weights and measures used by Kirwan in some
similar work. Writing to the latter under date of November 14,
1783, he said : 3 "It is therefore a very desirable thing to have
these difficulties removed, and to get all philosophers to use
pounds divided in the same manner, and I flatter myself that
may be accomplished, if you, Dr. Priestley, and a few of the
French experimenters will agree to it ; for the utility is so
evident that every thinking person must immediately be con-
vinced of it. My proposal is briefly this :
Let the philosophical pound consist of 10 ounces or 10,000 grains.
„ „ ounce „ „ 10 drachms or 1000 „
„ „ drachm „ „ 100 grains.
Let all elastic fluids be measured by the ounce measure of water,
by which the valuation of different cubic inches will be avoided,
and the common decimal tables of specific gravities will im-
mediately give the weights of these elastic fluids." Farther on
in the letter he says, " I have some hopes that the foot may be
fixed by the pendulum, and a measure of water, and a pound
derived from that ; but in the interim let us at least assume a
proper division which from the nature of it must be intelligible,
as long as decimal arithmetic is used."
1 Board of Trade Journal (London, Feb. 22, 1900), vol. xxviii. p. 449.
2 In 1620 Edmund Gunter had proposed a decimal measure for land with a
surveyor's chains of 100 links.
3 A. Siemens, Journal Institution of Elect. Engineers of Great Britain, vol. xxxiL
pp. 278-9.
THE METRIC SYSTEM IN EUROPE 99
A few days later (Nov. 23, 1783), Watt wrote to M. de Luc
calling attention to the difficulties of comparing the work of
investigators in different countries on account of the diversity in
weights, and also on account of " the absurd subdivisons used by
all Europe," even if the weights were the same. He describes
the plan outlined above, and suggests dividing the Paris pound
into 1000 parts. M. de Luc was asked to communicate with
Laplace on this subject, and three years later when Watt visited
Paris he met Lavoisier, Laplace, Monge, and Berthollet, whom we
have seen were deeply interested in the reform of weights and
measures. It is fair to assume that the subject was discussed by
Watt among them, and that they listened to the suggestions and
ideas of the English engineer, and this view is strengthened by
the provision inserted in the bill for the reform of the French
weights and measures that the French Academy and the Royal
Society appoint a joint committee to discuss universal weights
and measures.1
England, however, declined to co-operate with the International
Commission which examined the work of the French scientists on
which the metric system was based, and this attitude, as well as
a subsequent antipathy to the French system, was doubtles due
to the national feeling towards France. Mention, however,
should be made of the fact that in 1789 Sir John Riggs Miller
called the attention of Parliament to reforms in weights and
measures, moving for the appointment of a committee " to
investigate and report on the best means for adopting an
uniformity of weights and measures." He, too, had in mind the
length of the second's pendulum as a basis of linear measure, and
his plan was supported by the Rev. George Skene Keith, who
further urged that any new system should be a decimal one.
The desirability of a decimal system that should include not only
weights and measures, but also coinage, began to be felt, and in
1814 Sir John Wrottesley brought such a scheme to the notice of
Parliament. The result of the agitation was that in 1819 a
commission which included Dr. Thomas Young, William H.
Wollaston, and Captain Henry Kater reported adverse to the
adoption of the decimal scale, but the cause continued to be
1See M'Leod, "Notes on the History of the Metrical Measures and Weights,"
Nature (London, 1904), No. 1792, vol. lx. pp. 425-427.
100 EVOLUTION OF WEIGHTS AND MEASURES
argued, and at every discussion of changes in weights and
measures, the metric system had its advocates in increasing
numbers.
In 1816 a resolution was passed in Parliament providing for a
comparison of the imperial standard yard with the Trench
standard meter, this duty being assigned to the Eoyal Society.
That body received from Paris two platinum meters which had
been compared by Arago with the French standard. One was an
end standard which was exactly equal to the meter at the
temperature of melting ice, while the other was a line standard
which at the same temperature was short by "01759 mm. These
meters were carefully compared by Captain Kater with the
Shuckburgh scale, and when referred to the Parliamentary
standard the true length of the meter was determined at 39*37079
British inches, a value which was legalized by Parliament in its
Act of 1864 which permitted the use of the weights and measures
of the metric system.
Meantime the scientists and others had called for reforms in
the British system which would involve more than merely the
construction of new standards. In considering this subject, and
especially in its bearing on the adoption of a decimal system, a
committee of the House of Commons, reporting in 1862, stated
that " it would involve almost as much difficulty to create a
special decimal system of our own, as simply to adopt the metric
decimal system in common with other nations. And, if we did
so create a national system we would, in all likelihood, have to
change it again in a few years, as the commerce and intercourse
between nations increased, into an international one." The
scientific men, and those who had been careful observers at
international expositions and conventions, were now making their
influence felt, and in 1864 was passed the Act mentioned above,
which allowed the use of the metric system of weights and
measures. Not satisfied with this step, the metric advocates in
1868 proposed a bill making the system compulsory, but after a
second reading it was dropped. In the meanwhile the Standards
Commission, of which Sir G. B. Airy, the astronomer-royal, was
chairman, carefully studied the subject of weights and measures
for the kingdom, and their second report, dated April 3, 1869, is
devoted to the metric system
THE METRIC SYSTEM IN EUROPE 101
The status of the metric system was defined in 1878 by the
Weights and Measures Act, under the terms of which (clause 32)
the Board of Trade was authorized " to verify metric weights and
measures which are intended to be used for the purposes of
science or of manufacture or for any lawful purpose, not being
for the purpose of trade within the meaning of this Act."
The legislation of August 8, 1878, still left much to be desired,
and in 1895, in response to demands for further action, a com-
mittee was appointed from the House of Commons to investigate
the matter anew. This committee heard numerous witnesses and
carefully considered their testimony, giving ample opportunity for
both sides of the question to be discussed. In their report they
recommended :
" {a) That the metric system of weights and measures be at
once legalized for all purposes.
" (b) That after a lapse of two years the metric system be
rendered compulsory by Act of Parliament.
" (c) That the metric system of weights and measures be
taught in all public elementary schools as a necessary and
integral part of arithmetic, and that decimals be introduced at an
earlier period of the school curriculum than is the case at
present."
Parliament acted on that portion of the report providing for
the legalization of the metric weights and measures for all
purposes, passing a bill to that end May 27, 1897, but hesitated
when it came to making the system compulsory. On the
following year in an Order in Council dated May 19, 1898, after
an investigation by a committee of the Royal Society, the various
units were defined and their legal equivalents in the customary
weights and measures given. These differ by minute amounts
from those of the United States.
In 1903 it seemed to the members of the Decimal Association,
an influential organization which had been formed to further the
adoption of the metric system and of a decimal system of coinage,
that popular feeling in favor of radical reforms in the system of
weights and measures was increasing, and that it was an oppor-
tune time to make another attempt. Accordingly Lord Belhaven
and S ten ton introduced such a bill, which was supported on its
introduction by Lord Kelvin and later by Lords Rosebery,
102 EVOLUTION OF WEIGHTS AND MEASURES
Spencer, and Tweedmouth, and after a third reading was passed
and sent to the House of Commons, where, however, it was never
brought up for passage.
This bill was endorsed by a large number of town, city, and
county councils, and by over fifty chambers of commerce, includ-
ing some of the most important in the kingdom. Furthermore,
in addition to petitions from forty-two trades unions, representing
some 300,000 members, received while the bill was in the House
of Lords, there was a resolution unanimously passed by the
Congress of Trades Unions meeting at Leeds in September, 1904,
and representing some 5,000,000 workmen, in which it was
resolved to petition the House of Commons in favor of the bill.
There were also petitions from sixty Teachers' Associations,
Inspectors of Weights and Measures in eighty districts, and
thirty Ketail Trades' Associations, besides numerous Chambers
of Agriculture and Farmers' Associations. Thus it will be seen
that the bill was supported by eminently practical people as
well as scientists and theorists, and it is interesting to state that
in Great Britain retail tradesmen and workmen have been alive
to the many merits of the metric system.
The bill of 1904 provided for the establishment of the standard
kilogram and meter from the first day of April, 1909, as the
imperial standards of weight and of measure, though for sufficient
cause this date could be postponed by an Order in Council. It
also provided for Parliamentary copies of the substituted imperial
standards, and that future deeds, contracts, etc., must be in terms
of the metric system. The bill also made due provision for
various adaptations made necessary by the change, and prescribed
the general method in which it should be carried out.
In Australia an active demand was made for the introduction
of the metric system, and in 1905 it was proposed to introduce
into the Federation Parliament a bill with this object. In the
same year the neighboring colony of New Zealand adopted the
metric system as its legal system of weights and measures.
Great Britain, however, played an important part in the de-
velopment of scientific measures, namely, in working out the
C.G.S., or Centimeter-Gram-Second system, as was done by the
British Association for the Advancement of Science. This system
was based, as the name implies, on the metric units of length
THE METRIC SYSTEM IN EUROPE 103
and mass, and has been of the greatest benefit to science, being
universally adopted by physicists and engineers, and will be
found discussed more at length farther on in this volume.1
In Mexico the Metric System came into effect on the first
of January, 1862, in accordance with the terms of a law of
March 15, 1857, and a second law of March 15, 1861, which
provided for the exclusive use of the Metric Weights and
Measures for all purposes. While the new system was adopted
by the Government, yet private individuals did not take it
up, and there was needed an imperial decree, issued in Nov-
ember, 1865, which declared the Metric System alone valid
throughout the country. For a number of years the old and
new measures were used side by side, and also, with the
introduction of railways and of machinery for mining and other
purposes from the United States, the English foot and pound;
but gradually the Metric measures asserted their supremacy, and
now they are almost exclusively used. Mexico became a party
to the International Convention of Weights and Measures in
1890, and in 1896 it formally adopted the international standards
for the meter and kilogram.
Throughout South and Central America the Metric System
is largely employed, and in nearly all cases it is the legal
system of the different countries. There has been, however,
great difficulty in maintaining this system as the only one,
since in numerous instances the people have preferred to use
the older units derived from Spanish and other sources, while
exporters doing business with Great Britain and the United
States have made use of the Anglo-Saxon units. This, of
course, is due in great part to the lack of stability of the
South American governments, but conditions in this respect
are improving, and the use of the metric weights and measures
is now practically universal throughout South America. It
was on this account that representatives of these countries
assembled at the International American Conference at Washing-
ton in 1890 advocated the adoption by the United States of
the Metric Weights and Measures. Beyond the dates of
adoption, as given by the accompanying table, there is but
little to say as regards the individual countries
1 See Chapter ix. p. 205,
104 EVOLUTION OF WEIGHTS AND MEASURES
While in the foregoing paragraphs an attempt has been
made to summarize briefly when and how the metric system
was adopted by the more important nations of the world, it is
possible to obtain this information for the remaining countries
of the world by reference to the accompanying tables, which
indicate the time at which metric measures were first adopted,
when made compulsory, and, so far as can be ascertained and
briefly stated, the extent to which they have replaced other
and older measures. These tables speak for themselves, and
illustrate most forcibly the spread of the system. They are
based on a somewhat similar table published as an Appendix,
p. 67, of a Eeport from the Select Committee on the Weights
and Measures (Metric System) Bill [H.L.], May 5, 1904, to be
found among the Parliamentary Papers of that year, on the
Reports of British Consular officials abroad, to which reference
has already been made (see footnote, p. 91), and other official
sources of information.
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W H
CHAPTEK IV.
WEIGHTS AND MEASUKES IN THE UNITED STATES.
) In the early days of the American colonies the weights and
| measures, like the coinage, were based almost entirely on those
of the mother country, and where statutes were enacted pro-
viding for standards, these were derived from the standards
of the Exchequer of England. Inasmuch as that country was
the chief source of supply as well as a market for merchandise,
and the commercial dealings were very largely with its
inhabitants, such a condition was most natural, and inasmuch
as trade was not particularly extensive, such a system of
weights and measures amply sufficed.1 During the Eevolution,
however, it was realized that all possible means should be taken
to secure uniformity in commercial practices, and the need of
a single national system of money and weights and measures
was early appreciated. In the Articles of Confederation adopted
by the Continental Congress, November, 15, 1777, it was pro-
vided in section 4, article ix., that " The United States in
Congress assembled shall also have the sole and exclusive
right and power of regulating the alloy and value of coin
struck by their own authority, or by that of the respective
states ; fixing the standard of weights and measures throughout
the United States ; . . ." By the Federal Constitution, Congress
is explicitly given the power to fix the standard of weights
and measures, the fifth paragraph of section 8 of article i.
stating that the Congress shall have the power " to coin money,
1 See John Quincy Adams, " Report on Weights and Measures" (Washington,
1821), for summary of colonial, state, and territorial legislation, pp. 94-117.
110 EVOLUTION OF WEIGHTS AND MEASURES
regulate the value thereof and of foreign coins, and fix the
standards of weights and measures." It is somewhat curious
that the fixing of the standards of weights and measures is
almost the only power expressly and specifically conferred on
Congress which that body has refrained from exercising down
to the present time, notwithstanding its constant and most
active interest in the coinage of money, as evinced by a vast
amount of discussion and legislation.
In the days before and during the Eevolution the coinage of
various nations as well as from different state mints passed in
circulation, causing an inexpressible confusion of values and rates
of exchange, and it was but natural that uniformity and sim-
plicity should be desired. That this could best be attained by a
decimal system was appreciated as early as 1782, when Eobert
Morris, the Superintendent of Finance, an office corresponding to
that of the present Secretary of the Treasury, wrote to the
President of Congress " that it was desirable that money should
be increased in the decimal Eatio, because by that means all
calculations of Interest, exchange, insurance, and the like are
rendered much more simple and accurate, and, of course, more
within the power of the great mass of people. Whenever such
things require much labour, time, and reflection, the greater
number who do not know, are made the dupes of the lesser
number who do." x In accordance with the suggestions made, an
elaborate report on the question of a system of currency for the
United States was prepared by Thomas Jefferson, and on July 6,
1785, a decimal system of coinage was adopted.2 In the following
year, August 8, the complete system was duly determined, and
the amounts, nomenclature, and value of the various coins fixed.a
The success of the new currency was soon assured, and it received
favorable commendation both at home and abroad.
The reasons influencing its adoption would seem to have
demanded a similar system of weights and measures, and it is
perfectly evident that clear thinkers like Morris and Jefferson
1 Watson, History of American Coinage (New York, 1899), p. 10, quoting
from Wharton's Diplomatic Correspondence, vol. v. pp. 103-110.
2 See Watson, p. 16 ; also MS. Reports of Committee on Finance of the Continental
Congress, No. 26, pp. 537-560.
3 Journal of Congress, vol. xxxviii. No. 1.
WEIGHTS AND MEASURES IN UNITED STATES 111
were alive to its advantages; but even at these early times, as
well as subsequently, there was considerable disinclination on
the part of Congress to take any measure looking toward the
establishment or reform of these important adjuncts to commerce.
In fact, while there have been numerous suggestions on the
subject of weights and measures from Presidents in their messages,
there has been comparatively little legislation, and more has been
accomplished in the way of establishing and changing standards
oy Executive order than by direct legislation.
President Washington, however, early realized the importance
of the matter, and in his first speech or message to Congress,,
delivered January, 8, 1790, he said, " Uniformity in the currency,
weights, and measures of the United States is a subject of great
importance, and will, I am persuaded, be duly attended to."
Accordingly, the House of Eepresentatives referred the matter to
the consideration of the Secretary of State, Thomas Jefferson, and
requested him to prepare a report dealing with the subject. Mr.
Jefferson had been in Paris as Minister of the United States, and
doubtless was well acquainted with the measures to reform the
weights and measures of that country which had been and were
then under discussion. For this reason, as well as on account of
his connection with the establishment of the national currency on
a decimal basis, his selection was most fortunate, and within a
few months (July 4, 1790) a report was submitted containing two
complete and distinct plans.1 He suggested as the standard of
linear measure a uniform cylindrical rod of iron of such length
that in 45 degrees latitude at sea level and constant temperature
it should perform its vibrations in small and equal arcs in one
second of mean time. Such a rod would have a length of 58*72368
inches, corresponding to a length of a seconds' pendulum of
39*14912 inches. In one of the plans proposed he adapted the
existing system to this standard, thus securing uniformity and
stability, while in the other, which he considered available for
future use, he proposed a new and strictly decimal system which
was remarkably complete and comprehensive. Mr. Jefferson was
convinced of the utility of the decimal system, and in his proposed
scheme of weights and measures for the American people he aimed
1See The Works of Thomas Jefferson (edited by H. A. Washington, New York,
1884), vol. vii. pp. 472-495.
112 EVOLUTION OF WEIGHTS AND MEASURES
to reduce " every branch to the same decimal ratio already estab-
lished in their coins, and thus bringing the calculation of the
principal affairs of life within the arithmetic of every man who
can multiply and divide plain numbers." The success which has
attended the decimal currency of the United States shows that
•Jefferson was wise in his plan for a similar division for weights
and measures, and had his proposals been adopted much confusion
and inconvenience would have been spared the people of the
United States. Furthermore, but little difficulty would have
attended its adoption, as the fundamental unit, the foot, differed
but slightly from the foot then in use. This foot was derived by
Jefferson by taking one-fifth of the length of the rod forming the
second's pendulum and then employing multiples and sub-multiples
in building up a series of measures of length. A table of these
units would read as follows : 1
10 points make 1 line.
10 lines make 1 inch;
10 inches make 1 foot.
10 feet make 1 clecad.
10 decads make 1 rood.
10 roods make 1 furlong.
10 furlongs make 1 mile.
Naturally the squares and the cubes of these units formed the
units for area and volume, while for capacity the cubic foot was
selected forming the bushel, which was then divided and multi-
plied decimally to give other measures. Likewise the cubic foot
of water, which weighed 100 pounds of 10 ounces each, gave the
basis of the measures of weight, and these also were arranged
decimally. Hardly too much in praise of this system of Jeffer-
son's can be said, and its adoption by Congress would have
exerted a wonderful effect on metrology, not only in the United
States but also in the world at large. It will be remembered
that at this very time France was constructing its metric system,
while England, appreciating the confusion attending its complex
and unwieldy system of measures, was in good temper for a
change. Jefferson's system, although designed to have certain
points of contact with the then existing system so as to make
1 The Works of Thomas Jefferson (New York, 1884), vol. vii. p. 488.
WEIGHTS AND MEASURES IN UNITED STATES 113
it easy of adoption, nevertheless was perfectly uniform and
symmetrical, and while possibly less scientific and precise than
the French system, yet it possessed all the characteristic features
of convenience, symmetry, and completeness. Congress received
this able report, but did not adopt either of Jefferson's suggestions,
doubtless on account of the similar agitation for changes in
weights and measures then taking place in France and England,
and its desire to await their outcome.
The pressing need of some action for this country, neverthe-
less, was realized by the executive branch of the Government,
and again in his annual message to Congress on October 25, 1791,
President Washington reverted to the subject, stating that "A
uniformity in the weights and measures of the country is among
the important measures submitted to you by the Constitution ;
and, if it can be derived from a standard at once invariable and
universal, must be no less honorable to the public councils than
conducive to the public convenience."
A committee of the Senate appointed November 1, 1791, then
took the matter under advisement, and on April 5, 1792, presented
a report1 favoring the adoption of Jefferson's decimal plan, and
containing directions for the scientific construction of a standard
of length which would be divided into five equal parts, each of
which would correspond to a foot. The report also contained
information relative to the measures for the survey of land, units
of weights, etc. Several reports were submitted by this committee,
and it was finally decided (1793) " that the Standards should be
the mean of those found in the country." No legislative action
was taken by the Senate, and for several years there is apparently
no record of any great interest manifested in the subject by
Congress. In the meantime France had adopted the Metric
System with a hope that it would become universal, and on
January 8, 1795, the President transmitted to Congress a com-
munication2 from the Minister of the French Eepublic, describing
in detail the new system of weights and measures, the standards
of length and weight, and the method of dividing the standards
into decimal parts. A committee from the House of Eepresenta-
tives proceeded to study this plan, together with that of Jefferson,
1 Journal of the Senate, Second Congress, First Session, pp. 173, 174.
2 Executive Docs. , Third Congress, Second Session.
H
114 EVOLUTION OF WEIGHTS AND MEASURES
and reported in the following year ; but their recommendations
were of a general character, and involved experimental work by
scientists, which was never authorized by Congress. It may be
said in passing, Jefferson did not advocate the adoption of the
French system, as he did not approve of the use of a fundamental
unit derived from an arc of meridian in preference to the length
of a seconds' pendulum.1 As to his own plans, he was not a
zealous advocate of either of the propositions he had advanced,
and was willing to leave the entire matter to Congress.
The difficulties with France, the war with Great Britain, and
the consideration of various matters, political and otherwise, left
little time for Congress to act on matters of weights and measures,
and accordingly there was no legislative action for a number of
years. In the meantime the Coast and Geodetic Survey requiring
some standard of length, imported from England, in 1814, an
82-inch brass bar scale made by Troughton of London. Thirty-
six inches taken on this scale, between, divisions 27 and 63, were
adopted as the standard yard for the United States by the
Treasury, and this distance was used by other departments.2 The
meter, however, was selected at the outset for actual surveying
operations by the Coast and Geodetic Survey, and for this purpose
has since been continuously employed in its various triangulations.
The metric standards were a brass meter bar constructed in Paris
by Lenoir in 1813 for Mr. Hassler, and one of the original
secondary iron-bar standards constructed by the same maker for
the French Metric Committee in 1799, and presented to Mr.
Hassler by Tralles.3 This latter standard was employed by the
Coast Survey until the receipt of the international standards in
1890, and is now to be seen in the vault of the Bureau of
1 This is shown plainly in several of Jefferson's letters contained in the Works
of Thomas Jefferson (New York, 1884), particularly those to William Short
(vol. iii. p. 276), Dr. Robert Patterson (vol. vi. p. 11), and John Quincy Adams
(vol. vii. p. 87).
2 See F. R. Hassler, Report on Weights and Measures, Document 299, 22nd
Congress, 1st Session, 1832, p. 40. Also U.S. Coast and Geodetic Survey Report,
1877 ; Appendix 12.
3 See Hassler, loc. cit., p. 75, for translation of Tralles' description of these
standards. Also Transactions of American Philosophical Soc. (Phila., 1825), vol.
ii. p. 252 ; and Special Publication No. 4, U. S. Coast and Geodetic Survey, p. 31
(Washington, 1900).
WEIGHTS AND MEASURES IN UNITED STATES 115
Standards at Washington. It is of rectangular cross section
9 mm. x 29 mm., and is, of course, an end standard.
Eeforms in weights and measures were not proceeding any more
satisfactorily abroad than in the United States. Great Britain
had been unable " to reduce into any simple order the chaos of
their weights and measures,"1 as Jefferson wrote to Secretary of
State Adams in 1817, while in France the Metric System was not
securing the ready adoption that was desired. The countries
conquered by Napoleon and compelled to adopt it, returned to
their old ways once compulsion was removed; and even in France,
as we have seen, there was considerable doubt as to the practical
and ultimate success of the new system, while the decimal division
of time and the decimal measurement of the circle had proved
distinct failures. Therefore, it is not hard to explain the hesita-
tion in the United States about adopting the French system.
That some measures were needed we learn from the message of
President Madison to Congress in 1816, when he said:
" Congress will call to mind that no adequate provision has
yet been made for the uniformity of weights and measures con-
templated by the Constitution. The great utility of a standard
fixed in its nature, and founded on the easy rule of decimal pro-
portions, is sufficiently obvious. It led the Government at an
early stage to preparatory steps for introducing it, and a com-
pletion of the work will be a just title to the public gratitude."
Congress referred the matter to the Secretary of State, John
Quincy Adams, and that official undertook a thorough analysis
and study of the whole subject. To him Jefferson wrote in the
letter already quoted : 2 " I sincerely wish you may be able to rally
us to either standard, and to give us an unit, the aliquot part
of something invariable which may be applied simply and con-
veniently to our measures, weights, and coins, and most especially
that the decimal divisions may pervade the whole." Adams
realized that the matter was one of extreme importance that
could not be settled offhand, and on his own account examined
the question in all its many aspects, his conclusions being given
in a report3 submitted on February 22, 1821, that has since been
1 Works of Thomas Jefferson, vol. vii. p. 89.
2 Ibid.
3 J. Q. Adams, Report upon Weights and Measures, Washington, 1821.
116 EVOLUTION OF WEIGHTS AND MEASURES
considered almost a classic in American metrology. While the
Secretary of State was so engaged, a committee from the House
of Kepresentatives also considered the question of weights and
measures, and, January 25, 1819, submitted a report virtually
advising the adoption of the first plan proposed by Jefferson, and
recommending that models of the yard, bushel, and pound, con-
forming to those in most common use, be made under the
direction of a commission to be selected by the President, and
which, if satisfactory to Congress, should be declared the standard
weights and measures of the United States. Again, Congress
failed to take action on this recommendation, and when, two years
later, Secretary Adams submitted his report, in which he recom-
mended that no present change in the weights and measures of
the country be attempted, but that the standards should remain
as they were, that body had no disposition to oppose his sug-
gestions, and nothing was accomplished.
The report, however, is worth more * than passing notice, for
although Adams did not believe that the introduction of the
Metric System into the United States at that time was prac-
ticable, nevertheless he was as alive to its symmetry, complete-
ness, and general desirability, as he was to the many advantages
attending the introduction of a universal system of weights and
measures throughout the great countries of the world. While it
is, of course, impossible to do justice to the completeness and
philosophic treatment of the subject in this report by any
summary or brief extracts, nevertheless a few passages will show
how keen was Mr. Adams' understanding of the matter, and how
well he appreciated the advantages of the French system. He
said : ! " This system approaches to the ideal perfection of
uniformity applied to weights and measures, and whether destined
to succeed or doomed to fail, will shed unfading glory upon the
age in which it was conceived, and upon the nation by which its
execution was attempted, and has in part been achieved. In the
progress of its establishment there it has often been brought in
conflict with the laws of physical and of moral nature, with the
impenetrability of matter, and with the habits, passions, pre-
judices, and necessities of man. It has undergone various
important modifications. It must undoubtedly submit to others
1 J. Q. Adams, Report, p. 48.
WEIGHTS AND MEASURES IN UNITED STATES 117
before it can look for universal adoption. But, if man upon
earth be an improvable being ; if that universal peace, which was
the object of a Savior's mission, which is the desire of the
philosopher, the longing of the philanthropist, the trembling hope
of the Christian, is a blessing to which the futurity of mortal
man has a claim of more than mortal promise ; if the spirit of
evil is, before the final consummation of things, to be cast down
from his dominion over men, and bound in the chains of a
thousand years, the foretaste here of man's eternal felicity, then
this system of common instruments, to accomplish all the changes
of social and friendly commerce, will furnish the links of
sympathy between the inhabitants of the most distant regions ;
the meter will surround the globe in use as well as multiplied
extention, and one language of weights and measures will be
spoken from the equator to the poles."
As regards the metric or, as he terms it, the French system in
the abstract or as an ideal system, no one could be more
enthusiastic than Mr. Adams. He says : 1 " The single standard,
proportional to the circumference of the earth ; the singleness
of the units for all the various modes of mensuration ; the
universal application to them of decimal arithmetic ; the un-
broken chain of connection between all weights, measures,
moneys, and coins; and the precise, significant, short, and
complete vocabulary of their denominations : altogether forming
a system adapted equally to the use of all mankind ; afford such
a combination of the principle of uniformity for all the most
important operations of the intercourse of human society ; the
establishment of such a system so obviously tends to that great
result, the improvement of the physical, moral, and intellectual
condition of man upon earth ; that there can be neither doubt
nor hesitancy in the opinion that the ultimate adoption and
universal, though modified, application of that system is a con-
summation devoutly to be wished."
The strongest praise for the French system is for the time
that it will save, and here Mr. Adams states,2 " Considered
merely as a labor-saving machine, it is a new power offered
to man incomparably greater than that which he has acquired
by the new agency which he has given to steam. It is in
1 J. Q. Adams, Report, p. 90. 2Ibid., p. 91.
118 EVOLUTION OF WEIGHTS AND MEASURES
design the greatest invention of human ingenuity since that
of printing."
Mr. Adams, while he realized the desirability of universal
measures, believed that they could only come " by consent and
not by force," and mindful of the difficulties attending the intro-
duction of the metric system in France, and of certain of its
features being susceptible of further improvement, thought it to
be the best policy for the United States first to confer with
foreign nations as regards the future and ultimate establishment
of universal and permanent uniformity, and, meanwhile, to
secure for the weights and measures in use throughout the
United States a more perfect uniformity by suitable legislation
especially avoiding for the time being any innovations. The
conclusion of the report is no less interesting than its other
sections : It states,1 " France first surveyed the subject of weights
and measures in all its extent and all its compass. France first
beheld it as involving the interests, the comforts, and the morals
of all nations and of all after ages. In forming her system she
acted as the representative of the whole human race, present and
to come. She has established it by law within her own terri-
tories, and she has offered it as a benefaction to the acceptance of
all other nations. That it is worthy of their acceptance is
believed to be beyond question. But opinion is the queen of the
world, and the final prevalence of this system beyond the
boundaries of France's power must await the time when
the example of its benefits, long and practically enjoyed, shall
acquire that ascendancy over the opinions of other nations
which gives motion to the springs and direction to the wheels
of power."
It is doubtful if a stronger statement of the abstract merits of
the metric system could be made than is contained in this report.
Mr. Adams, however, was in error in believing that concerted
action was necessary to secure the adoption of a universal system,
as it has come about gradually, and has been adopted by the
various nations of the world at such times as seemed to them
suitable and convenient. Again, experience has shown the error
of Mr. Adams' view on the decimal division of the United States
coinage. He says (page 81), "The convenience of decimal
lJ. Q. Adams, Report, p. 135.
WEIGHTS AND MEASURES IN UNITED STATES 119
arithmetic is in its nature merely a convenience of calculation ;
it belongs essentially to the keeping of accounts ; but it is merely
an incident to the transactions of trade. It is applied, therefore,
with unquestionable advantage to moneys of account, as we have
done : yet even in our application of it to the coins, we have not
only found it inadequate, but in some respects inconvenient."
This famous report has been quoted most extensively by
writers on American metrology, and passages are cited with great
enthusiasm by both metric and anti-metric advocates in support
of their respective positions. While conceding its great breadth
and philosophical character, yet at the present time it is worth
considering whether too much stress has not been laid on this
celebrated document. Although President Adams was a zealous
student, errors of statement are to be noted, while at the same
time advances in the science of metrology have made it necessary
to look at certain matters in a new light.
There was at least one department of the U.S. Government —
namely, the Mint — where any uncertainty of weight could not for
obvious reasons be tolerated. Accordingly, Minister Gallatin
was instructed to procure from England a copy of the imperial
standard Troy pound which had been adopted in 1825. This he
did, and the standard, after having been most carefully compared
by Captain Kater, was transmitted to the United States, and by
Act of Congress of May 19, 1828,1 was duly established as the
coinage standard of the United States, the Act being remarkable
in that it is the only legislative Act legalizing any of the
•customary measures, and establishing a standard for such purpose.
The Act provides, that " For the purpose of securing a due con-
formity in weight of the coins of the United States to the
provisions of this title, the brass troy -pound weight procured by
the minister of the United States at London, in the year eighteen
hundred and twenty-seven, for the use of the Mint, and now in
the custody of the Mint at Philadelphia, shall be the Standard
troy pound of the Mint of the United States, conformably to
which the coinage thereof shall be regulated." 2
1C. 131, Sec. 50, 17 statutes 432. Revised statutes 3548.
2 A description of this standard, together with the various certificates of
individuals concerned with its construction, testing, receipt, etc., including
Oaptain Henry Kater, Minister Gallatin, and President John Quincy Adams,
120 EVOLUTION OF WEIGHTS AND MEASURES
On May 29, 1830, the Senate passed a resolution ordering the
comparison of the standards of weights and measures used by the
different custom-houses, and when these measures or copies were
called in to the Treasury Department for examination, it was
found that there was the greatest lack of uniformity throughout
the various customs districts. In many cases the various state
or local sealers of weights and measures were appealed to not
only for purposes of comparison, but even for the correction of
the standards.1
The resulting diversity of weights and measures naturally was
not without its effect on the revenues of the Government, in
addition to violating that section of the Constitution which pro-
vides that taxes shall be uniform throughout the United States.
The national standards upon which the measurements made in
the custom-houses were based are thus described in the following
extract from the report of S. D. Ingham, Secretary of the
Treasury, March 3, 1831 :
" Among the instruments which had been procured, some years
ago, under the direction of the President, for the survey of the
coast, was a standard measure of length, exactly corresponding
with the British Parliamentary standard, as established in 1758,
with which that of 1760 is identical, as tested by Sir George
Shuckburgh in 1798, and by Captain Kater in 1821, on the
occasion of the last determination of the weights and measures in
England, when it was adopted as the legal unit. This standard
measure has, by means which will be explained in a future
report, been compared with the pendulum vibrating seconds in
London, and also with the French meter, which is based upon
measurements of arcs of a meridian of the earth. With such,
evidence of its character, and such an opportunity of correcting
any alteration by reason of decay, it was without hesitation,
adopted as the unit for the comparison of measures of length.
" The troy pound used in the Mint is known to be identical
with the latest established standard troy pound of Great Britain,
as regulated by the British laws, and standarded by Captain
will be found contained in an interesting history of the weights and measures of
the United States, by 0. H. Tittman, in the United States Coast and Geodetic
Survey Report for 1890, Appendix 18, pp. 736-8.
1Hassler, p. 6 (House of Reps. Doc., No. 299, 22nd Congress, 1st Session).
WEIGHTS AND MEASURES IN UNITED STATES 121
Kater in 1824, having been constructed by him at the special
request of Mr. Gallatin, upon the same principles and in the
same manner that he had employed in the construction of the
British standard." 1
Preparations were duly made to construct from these standards
the standards for the custom-houses, and on June 14, 1836, a joint
resolution was adopted by both Houses of Congress providing
that there should be constructed in the office of the Coast
Survey for every state and territory, complete sets of standards
equal to those made for the custom-houses, " to the end that
a uniform standard of weights and measures may be established
throughout the United States," and in July, 1838, it was ordered
that balances for the accurate comparison of weights should be
similarly constructed and distributed to the states and territories.
The standard weights were given to the custom-houses in 1836,
and in the following years the standard yards, which were based
on the Troughton scale, and liquid measures were distributed.
By 1856 the various states of the Union were supplied with
sets of standards, and shortly after their receipt the individual
states enacted statutes establishing them as the standards of
weights and measures.2 This work was important, as being
the first practical and systematic attempt to secure general
uniformity of weights and measures throughout the country,,
and as an early example of refined constructive scientific work
being carried on by the national government for the benefit
of the people at large in their commercial relations.
It should be said in passing that the early work of estab-
lishing the standards of weights and measures for the United
States was done by Professor F. E. Hassler, the superintendent
of the Coast Survey, from its inception to his death, and during
these years many interesting reports dealing with the scientific
and other features of the work were prepared by him.3 To
Extract from the report of S. D. Ingham, Secretary of State, March 3, 1831 1
House of Representatives, Doc. No. 299, July 2, 1832, 22nd Congress, 1st
Session.
2 See Laws Concerning the Weights and Measures of the United States, an official
compilation of the United States Bureau of Standards of legislation on this-
subject (Washington, 1904).
3 See partial bibliography in House of Representatives, Report No. 3005, 56th
Congress, 2nd Session.
122 EVOLUTION OF WEIGHTS AND MEASURES
Professor Hassler was due the derivation of the standard avoir-
dupois pound from the standard Troy pound, and so accurately
was the work accomplished that when the British Government
sent over in 1856 a copy of the standard avoirdupois pound, there
was found a difference of '001 of a grain between British and
American standards. He also connected the units of capacity
with those of weight, by using in his experiments, which were
begun in 1830, distilled water at its temperature of maximum
density, and thus was able to determine and construct accurate
standards.
On the death of Mr. Hassler in 1843, Professor A. D. Bache
became the head of the Coast Survey, and manifested consider-
able interest in the work of the Office of Weights and Measures,
supervising the completion and distribution of the state standards
begun by Mr. Hassler, and in his reports making recommenda-
tions looking towards the improvement of the United States
system of weights and measures, and also the establishment of
a universal system.
With the distribution of the standard weights and measures,
there resulted the natural inquiries as to their origin and value,
and the legal enactments upon which they were founded. Pro-
fessor Bache in his report for 18481 summarizes the essential
facts relating to them. The actual standard of length is the
8 2 -inch Troughton scale (which has been already described) ;
" the units of capacity measure are the gallon for liquid and the
bushel for dry measure. The gallon is a vessel containing
58,372*2 grains (8*3389 pounds avoirdupois) of the standard pound
of distilled water, at the temperature of maximum density of
water, the vessel being weighed in air in which the barometer
is 30 inches at 62° Fahrenheit. The bushel is a measure
containing 543,391 '89 standard grains (77'6274 pounds avoir-
dupois) of distilled water at the temperature of maximum
density of water, and barometer 30 inches at 62° Fahrenheit."
The gallon is thus the wine gallon of 231 cubic inches nearly,
and the bushel the Winchester bushel nearly. The temperature
of maximum density of water was determined by Mr. Hassler
to be 39'85° Fahrenheit. The standard of weight is the Troy
pound copied by Captain Kater in 1827 from the imperial Troy
^Oth Congress, 1st Session, Senate Executive Doc. 73 (1848), p. 8.
WEIGHTS AND MEASURES IN UNITED STATES 123
pound for the United States Mint, and preserved in that
establishment. The avoirdupois pound is derived from this :
its weight being greater than that of the Troy pound, in the
proportion of 7000 to 5760 ; that is, the avoirdupois pound is
equivalent in weight to 7000 grains Troy. The multiples, as well
as subdivisions of the pound, are based upon this standard, the
weight of which was determined by the best means attainable at
that time, in grain weights, by Troughton, at the Mint, and at
the Office of Weights and Measures, in presence of Mr. Hassler,
and of the Director of the Mint, Dr. Moore. From these
determinations resulted the pound weights of the Office of
Weights and Measures, which are therefore copies of the Troy
pound of the United States Mint or derived from it. The
pound is a standard at 30 inches of the barometer and 62°
Fahrenheit thermometer. The Troy pound of the Mint was
found, in the comparisons of Captain Kater, to be heavier than
the imperial Troy pound by only '0012 of a grain.
" The measures of length and capacity, and the weights just
referred to, have been adopted by the Treasury Department as
standards for the measures and weights of the custom houses of
the United States, and reported as such to Congress in 1832. . ."
That the system was then unsatisfactory in many respects we
have abundant testimony. The simplification of the existing
weights and measures, and the issuing of correct standards had
been provided for as Adams had suggested, but nothing had been
done to improve the system or towards co-operating with foreign
nations in establishing a universal system, as Adams had also
suggested. On the conditions as they then existed Professor
Bache's observations are of interest. In a report made in 1848
he says : x
" No one who has discussed the subject of weights and
measures in our country has considered the present arrangement
as an enduring one. It has grown up with the growth of
European society, and is deficient in simplicity and in system.
The labor which is expended in mastering the complex denomi-
nations of weights and measures is labor lost. Every purpose
for which weights and measures are employed can be answered
by a simple and connected arrangement."
1 Executive Document 84, Thirteenth Congress, 1st Session, July 30, 1848.
124 EVOLUTION OF WEIGHTS AND MEASURES
Professor Bache believed that inasmuch as it was the prac-
tically universal opinion of all who had studied and written on
American weights and measures that the system then in use
must be considered temporary, and eventually be replaced by a
more convenient and systematic arrangement, and wrote in
reference to Adams' plan for an international conference on the
subject as follows : " The present time seems especially to invite
an effort of this kind. In England the subject of weights and
measures is under consideration by a commission ; and on the
Continent the new relations of states hitherto separated appears
to be favorable to this object. Such changes can be readily
effected by suitable means in one generation, by introducing the
new measures through the elementary schools." In a subsequent
report Professor Bache asks, " Has not the time arrived, in the
general progress of commercial and international intercourse, and
the rapid advance of our own country in science, wealth, and
power, when her voice should be heard in an important matter
like this ? Should not Congress make the proposition to all
nations, to meet, by their representatives, and consult for the
purpose of establishing uniformity of weights and measures ?
Such action could not fail to meet with a response due to the
greatness of the subject, and if the great object be attained, to
lead to results productive of vast and lasting benefit to the
human race."
While it is quite natural that opinions in favor of the adoption
of the metric system should be given by officials of the bureau of
weights and measures, and by Secretaries of the Treasury, it is
possible to recognize the beginning of a distinct general feeling
and movement in favor of reforms in American weights and
measures. This may be traced largely to the increasing numbers
of scientific and professional men who were sent to Europe for
education, and, who having used the metric system in the schools
and laboratories of France and Germany, became enthusiastic
advocates of the system, with the result that on their return
to the United States they adopted it for their own scientific
work, and taught it to their students. In chemistry especially
its pre-eminence was early recognized, and American chemists
soon fell in with the universal system which by this time
was employed in all the European journals and standard
WEIGHTS AND MEASURES IN UNITED STATES 125
works.1 American diplomats and representatives to various inter-
national conferences also became convinced of the desirability of
a uniform system of weights and measures, and their influence
was also exerted in stimulating a feeling in favor of reforms.
In February, 1854, the American Geographical and Statistical
Society, of which George Bancroft, the historian and Minister to
Spain, was then president, presented a memorial to Congress in
which the appointment of a joint scientific commission to consider
a uniform system of weights and measures based on a decimal
system was urged. This was one of the earliest of a number of
similar resolutions which have since been addressed to Congress.
Of more importance, however, as coming from the people at large
rather than from scientific bodies, were the resolutions adopted
by the legislatures of various States. The legislature of New
Hampshire, by joint resolution approved on June 28, 1859, re-
quested their senators and representatives to urge upon Congress
the adoption of a decimal system, while the legislature of Maine,
March 20, 1860, by joint resolution, expressed in still more
decided language, their desire for a uniform international system
of weights, measures, and coins. This action was soon followed
by a similar resolution by the legislature of the State of Con-
necticut, which in June, 1864, took an important step in recom-
mending to the proper school officers, that they should provide
for the teaching of the metric system in all the schools of the
State. From this time interest in the metric system in con-
nection with the study of the arithmetic in the schools increased,
so that the pupils within a few years became aware of the
existence of the system, although often in the method of pre-
sentation of the subject in text-books, and by teachers there was
little to commend it to the young mind. The problems were
usually those involving conversion from the common system to
the metric, and as such, were not likely to inspire any great
degree of appreciation for the latter.
The Civil War so occupied the legislative and executive
departments of the Government that there was little opportunity
1 The use of the metric measures in American College text-books, in physics and
chemistry, dates from 1868-1870. In similar works for high schools the new
system was used from 1878. R. P. Williams before Am. Chem. Soc, June,
1900.
126 EVOLUTION OF WEIGHTS AND MEASURES
for any marked progress on the part of Congress or the officials.
The condition of affairs is stated by Salmon P. Chase, Secretary
of the Treasury, in his annual report December 9, 1861, where he
writes : " The Secretary desires to avail himself of this oppor-
tunity to invite the attention of Congress to the importance of a
uniform system and a uniform nomenclature of weights and
measures, and coins to the commerce of the world in which the
United States already so largely shares. The wisest of our
statesmen have regarded the attainment of this end so desirable
in itself as by no means impossible. The combination of the
decimal system with appropriate denominations in a scheme of
weights, measures, and coins for the international uses of com-
merce, leaving, if need be, the separate systems of nations
untouched, is certainly not beyond the reach of the daring genius
and patient endeavor which gave the steam engine and the
telegraph to the service of mankind. The Secretary respect-
fully suggests the expediency of a small appropriation to be
used in promoting interchange of opinions between intelligent
persons of our own and foreign countries on this subject."
In 1863 the United States was represented abroad at two
important international congresses, both of which took action on
the matter of weights and measures which commended itself to
the American delegates. At the International Statistical Con-
gress held at Berlin, a committee appointed at the Paris meeting
three years previously, to consider the question of uniform
international weights, presented a report in which the subject
was carefully considered and as a result of which the Congress
resolved that the same measures for international commerce was
of the highest importance, and that the metric system was the
most convenient of all that could be recommended for inter-
national measures.1 At a previous session this body had
recommended that the countries which employed weights and
measures other than the metric should give in adjoining columns
the metric equivalents of all statistics.
The other international congress referred to was a postal
congress held at Paris in May, 1863, and which resulted in
important measures towards securing uniformity of weights
1 Samuel B. Ruggles, Report on International Statistical Congress at Berlin in,
respect to Uniform Weights, Measures, and Coins (Albany, 1864), pp. 43, 44.
WEIGHTS AND MEASURES IN UNITED STATES 127
throughout the world. It was here recommended, that, " Sec. 7.
The rates upon international correspondence shall be established
according to the same scale of weight in all countries," that
" Sec. 8. The metrical system, being that which best satisfies the
demands of the postal service, should be adopted for international
postal relations, to the exclusion of every other system " ; and
that " Sec. 9. The single rate upon international letters shall be
applied to each standard weight of 15 grams or fractional part of
it." This proposition proved satisfactory to the various nations
and accordingly was incorporated in the International Postal
Convention.
In 1866, when the resolutions authorizing the use of the
metric system of weights and measures was passed by the
Congress of the United States, which is referred to at more
length below, an Act was also passed enabling the Post Office
Department to use the metric weights and measures for foreign
and other purposes, and the law was re-enacted in 1872 and
now reads {Revised Statutes of the United States, Sec. 3880),
" The Postmaster-General shall furnish the post-offices ex-
changing mails with foreign countries, and to such other
offices as he may deem expedient, postal balances denoted in
grams of the metric system, fifteen grams of which shall be
the equivalent for postal purposes of one half ounce avoirdupois,
and so on in progression." The interchange of mail by all
the civilized countries of the world represents the most extensive
use of a uniform system of weights and measures in the world
and has been carried on for many years without the slightest
confusion or embarrassment. All mail matter transported be-
tween the United States and the fifty or more nations,
signatories of the International Postal Convention, including
the United States and Great Britain even, is weighed and paid
for entirely by metric weight.
The serious consideration of the metric system in the United
States by the people at large may be said to date from 1866
when Congress passed a Bill which was approved by the
President authorizing the use of the metric system of weights
and measures. In this action Congress had the advice of
the National Academy of Science, which had appointed in
1863, at the request of the Secretary of the Treasury, a special
128 EVOLUTION OF WEIGHTS AND MEASURES
committee to consider the matter. In its report, which was
adopted by the Academy, occurs the following passage, which
seems to sum up the situation : " The committee are in favor
of adopting, ultimately, a decimal system : and in their opinion,
the metrical system of weights and measures, though not
without defects, is, all things considered, the best in use.
The committee therefore suggest that the Academy recommend
to Congress to authorize and encourage by law the introduction
and use of the metrical system of weights and measures, and
that, with a view to familiarize the people with the system,
the Academy recommend that provision be made by law for
the immediate manufacture and distribution to the custom-
houses and States, of metrical standards of weights and
measures : to introduce the system into the post-offices by
making a single letter weigh 15 grammes instead of 14^^,
or half an ounce : and to cause the new cent and two cent
pieces to be so coined that they shall weigh respectively
5 and 10 grammes, and that their diameters shall be made
to bear a determinate and simple ratio to the metrical unit
of length."1 Accordingly, by the law of May 16, 1866, the
weight of the 5 cent copper nickel piece was fixed at 5 grams.
This idea was extended to the silver coinage, and by the law
of Feb. 12, 1873 {Revised Statutes of the United States, Sec.
3513), it was provided that "The weight of the half dollar
shall be twelve grams and one-half of a gram; the quarter
dollar and the dime shall be, respectively, one-half and one-
fifth of the weight of said half dollar." The Act passed
by Congress (Revised Statutes of the United States, Sec. 3569)
on July 28, 1866, making the metric system permissive, pro-
vided that "it shall be lawful throughout the United States
of America to employ the weights and measures of the metric
system, and no contract or dealing, or pleading in any court,
shall be deemed invalid or liable to objection because the
weights and measures expressed or referred to therein are
weights or measures of the metric system." The Act further
provided a series of legal tables of equivalents, and upon them
are based in the United States all conversions from one system
1 House of Representatives, Report of the Committee on Coinage, Weights,
and Measures, 46th Congress, 1st Session, Report No. 14, p. 23, part i.
WEIGHTS AND MEASURES IN UNITED STATES 129
to the other, as, for example, those contained in the tables in
the Appendix of this book. To further the use of the metric
system Congress passed an Act, approved July 27, 1866,
authorizing and directing the Secretary of the Treasury to
furnish to each State one set of the standard weights and
measures of the metric system. With this start the metric
system has grown in the United States, and various measures
looking towards its final adoption have been urged in Congress
and among the people generally.
The delegates to the Paris Exposition of 1867 were par-
ticularly enthusiastic in this respect, and among them Professor
F. A. P. Barnard, President of Columbia College, who, with
.a number of other advocates of reforms in weights and measures,
formed December 30, 1873, the American Metrological Society,
and was its president until his death in 1889.1 This society,
while interested in such kindred subjects as the adoption
of standard time and international currency, carried on an
active propaganda in behalf of the metric system, while the
Metric Bureau which was organized July, 1876, with head-
quarters in Boston, supplied material both in the way of
literature and actual weights and measures, charts, tables,
etc., that was of the greatest assistance to the general public,
especially teachers, who were now called upon in many States
to explain and teach the principles of the system.
Sufficient interest was manifested in the subject for the United
States Government to accept the invitation of the Government
of France to send delegates to Paris to form an international
commission to construct new metric standards. America was
accordingly represented by Professor Joseph Henry and J. E.
Hilgard, the latter being an active member of various important
committees concerned with the construction of the standards.
When this commission, after reassembling in 1872, decided that
an International Bureau of Weights and Measures should be
established in Paris, the plan had the approval of the delegates
of this country and of the American scientific world generally,
the National Academy of Sciences formally favoring the scheme
and recommending to the Government the signing of such
a treaty. The work of the Commission has already been
aSee Proceedings, American Metrological Society, 1873-1888 (New York).
I
130 EVOLUTION OF WEIGHTS AND MEASURES
discussed,1 and in this connection it is necessary merely to record
the fact that when the American Minister to France, Mr. E. B.
Washburne, signed the convention, together with delegates from
sixteen other nations, agreeing to establish and support the
International Bureau of Weights and Measures, the United
States became committed to the principle of international weights
and measures, and privileged to participate in the benefits accru-
ing from a common system and common standards.
In 1889, after accurate and careful construction and adjustment
and comparison, the international prototype standards of the
standard meter and kilogram were completed by the bureau, and
were distributed to the various countries supporting the Com-
mission. In a distribution by lot, the United States received
meters Nos. 21 and 27, and kilograms Nos. 4 and 20. The seals
of meter No. 27 and kilogram No. 20 were broken by President
Benjamin Harrison on January 2, 1890, and they were straight-
way deposited in a fireproof room at the Office of Weights and
Measures in the Coast Survey Building.2 These standards were
immediately adopted as the national prototype meter and kilo-
gram, and the primary standards for the United States, and were
employed as fundamental standards for deriving customary
units, the yard and the pound, as well as for constructing and
standardizing secondary metric standards. To obviate any
possible misunderstanding, however, a formal order, approved by
the Secretary of the Treasury, was issued on April 5, 1893,
recognizing " the International Prototype Meter and Kilogram
as fundamental standards, and the customary units, the yard and
the pound, will be derived therefrom in accordance with the Act
of July 28, 1866." 3
Here, again, we find a matter of fundamental importance
settled by Executive order, and the United States firmly com-
mitted to the metric system as the basis of all measures in use,
1 See pp. 72-77. For text of treaty, diplomatic correspondence, reports, etc ,
see chapters ii. and iv., Report No. 14, 46th Congress, 1st Session, House of Repre-
sentatives, Committee on Coinage, Weights, and Measures (Washington, 1879).
2 For technical description of the standards, certificates, reports, etc., consult
Report U.S. Coast and Geodetic Survey, 1890, Appendix 18, pp. 746-758.
3 Bulletin No. 26, U.S. Coast and Geodetic Survey, "Fundamental Standards
of Length and Mass." Republished as Appendix No. 6, 1893, U.S. Coast and
Geodetic Survey Report.
WEIGHTS AND MEASURES IN UNITED STATES 131
no matter what their source. So far as fundamental standards
go, the only ones used by the United States are metric and
international, and to them must be referred all measures, whatever
their nature. These standards are known in their relation to
the standards of the International Bureau at Sevres, and to
those of the various foreign countries, so that in case of their
destruction they could readily be reproduced, thus guaranteeing
the permanency of weights and measures founded upon them.
In fact, meter No. 27 was transported to Paris in 1904 for
comparison with the standards of the International Bureau,
and after several series of careful observations its value was
redetermined in terms of the international standard prototype.
It was found that No. 27 at 0° centigrade was too short by
2 microns, a discrepancy greater by '55 microns than that
obtained in 1888, when it was tested with the other national
prototypes. This change, however, was so minute that the
U.S. Bureau of Standards decided to employ the old value
in all of its determinations until an opportunity had been
given to compare standard No. 27 directly with the international
prototype meter and with other national prototypes. Inasmuch
as the relation of No. 27 to No. 21 is accurately known, as
also are the values of various secondary standards in terms
of both national standards, it will be seen that the Bureau
of Standards is now in a position to guarantee the accuracy
and permanency of the measures of the United States.1
That progress was being made in the use of the metric system
is shown by the fact that when Congress, on March 3, 1893,
passed an Act2 establishing a standard scale for the measurement
of sheet and plate iron and steel, it was expressed in terms of
both the customary and metric measures. Of perhaps greater
importance was the Act approved July 12, 1894 {Revised
Statutes of the United States, Supplement, vol. ii. chap. 131,
1894), which denned and established the units of electrical
measure. These were the international electrical units based on
1See L. A. Fischer, " Recornparison of the United States Prototype Meter,"
Bulletin of the Bureau of Standards (Washington), pp. 5-19, No. 1, vol. i.
1904. The discrepancy mentioned has since been accounted for through a
small error in the coefficient of expansion of No. 27, which was compared at
different temperatures in 1888 and 1904.
2Bevised Statutes, 3570, c. 231, Sec. 1, 27 Statute, 746.
132 EVOLUTION OF WEIGHTS AND MEASURES
the metric system which were in use by electrical engineers
throughout the world, having been definitely settled at a congress
held at Chicago in 1893.1
In 1901 the National Bureau of Standards was established by
Act of Congress to take over the duties of the old Office of
Weights and Measures of the Coast and Geodetic Survey, and
to have somewhat broader functions, especially in carrying on
standardization and other scientific work of general public
advantage. To this bureau was assigned the custody of the
national standards and the construction and comparison of
secondary and other standards of weights and measures of all
kinds. In the event of the adoption of the metric system, it
would fall to this bureau to oversee the construction and certify
to the correctness of the many new standards that would be
required in science, commerce, and the arts. This it is well
equipped to do, and has large laboratories with every facility for
such work.
When new territories were added to the United States as a
result of the Spanish war in 1898, it was found that the metric
system of weights and measures was employed in both Porto
Eico and the Philippine Islands, and the status of the system in
these possessions was duly confirmed. In the proclamation of
the Military Governor of Porto Rico, March 18, 1899, it was
stated, " 1. The use of the metrical system of weights and
measures and its nomenclature are obligatory. 2. Its use is
enforced in all transactions, sales, contracts, ... 3. Wholesale
and retail mercantile establishments shall sell their goods to
the public conformably to the metric system." The Political
Code of Porto Rico (1902), sections 230-246, definitely fixes the
metric systems and gives the legal definitions. The Philippine
Tariff Act (No. 230, September 17, 1901, sec. 9) contained a pro-
vision that " The metrical system of weights and measures as
authorized by sections 3569 and 3570 of the Revised Statutes of
the United States, and at present in use in the Philippine
Islands, shall be continued." In the Government Bill of 1902 it
was provided that " Sections (of the former2 Act) are hereby
amended by reducing all measurements therein, whether of dis-
tance, area, or value, to the metric system."
1 See p. 208, chap. ix. 2 Philippine Government Act of 1902.
WEIGHTS AND MEASURES IN UNITED STATES 133
Since the first permissive legislation in 1866 there have been
various Bills introduced into Congress to establish the metric
system, and each successive one has come before Congress with
stronger support, and likewise with stronger opposition on the
part of those opposed to any change. The matter of weights and
measures has been investigated most carefully by various House
Committees on Coinage, Weights, and Measures, and their reports
are replete with information on the subject treated from different
standpoints. In 1896 two interesting reports1 were prepared
after the committee had made a careful consideration of the
subject extending over two sessions, and a Bill to establish the
metric system was unanimously recommended for adoption,
but, however, did not pass a third reading. Again in 1901 a
somewhat similar Bill was reported from the Committee, accom-
panied by a brief report 2 in which its passage was recommended,
but unfortunately this Bill was received too late to be considered
by the Congress then in session. Once more, in 1902 and 1903,
the subject was discussed in committee and numerous hearings
were held, the record of which was embodied in an interesting
report3 in which the establishing of the metric weights and
measures as the legal standards of the United States was
recommended.
The general tendency of all these Bills was the same. It was
proposed that within a few months after their passage, usually
at the commencement of the next calendar year, that the national
Government in all its business relations, as well as in all its
constructive work, should adopt the metric weights and measures
exclusively, while for the public at large two or three years
should elapse, after which they would become the legal system
of the country. It was not proposed to resort to compulsory
measures, but to so establish the new system that it would
gradually extend into universal use. In the Littauer Bill intro-
duced in 1905 it was provided only that the metric system
should be employed by the Government in all its transactions
and activities.
^H.R. Report No. 795, and H.R. Report No. 2885, February 10, 1897,
54th Congress.
2 H.R. Report No. 3005, 56th Congress, 2nd Session, March 1, 1901.
ZH.R. Report No. 1701, 57th Congress, 1st Session, April 21, 1902.
134 EVOLUTION OF WEIGHTS AND MEASURES
Secretaries of State and Treasury, irrespective of political
party, as well as other executive officers of the Government, have
urged the adoption of the international system, and diplomats
and consuls have repeatedly called attention to the benefits to
commerce that would ensue. Scientific men and educators have
unanimously urged the desirability of the change, as have many
engaged in foreign commerce. Against any innovation at the
present time are many manufacturers and mechanical engineers,
many of whom have secured in their work a considerable accu-
racy of construction, especially as regards patterns based on the
English measures, which they assert could only be abandoned at
an expense entirely incommensurate with any possible benefit.1
At Congressional hearings, in the scientific press, and at meetings
and conventions, the question has been thoroughly debated by
those interested, and the material for information is most ample.
It is now, however, a matter for the American nation at large,
and when the people are thoroughly convinced of the great
benefits that will ensue, there will be no outcry against temporary
inconvenience. The adoption of the metric system is surely in
the line of progress, and when once it is realized, the United
States, with its superior school system and general high order of
intelligence possessed by its people, especially its workers, can
make the change with a minimum of embarrassment and can
avail themselves of its benefits more quickly than has been done
in the past by European nations.
1 This point of view will be found strongly represented in Halsey and Dale,
The Metric Fallacy, New York, 1903, one of the ablest of the anti-metric books,
and one that attracted considerable attention at the time of its publication on
account of the bitterness of its attacks on the metric system and its advocates.
It furnished material for many reviews and discussions in the technical press,
both favorable and hostile. Of the latter possibly the most interesting and able
were those in the Electrical World and Engineer (New York), vol. xliv. No. 19,
pp. 784-794, Nov. 5, 1904, and in The Physical Review (Ithaca), 1904.
A somewhat more scholarly, though less argumentative paper from a
similar point of view, by George W. Colles, entitled " The Metric versus the
Duodecimal System," will be found in the Transactions of the American Society of
Mechanical Engineers, vol. xviii. pp. 492-611, 1896-1897. See also a paper by
J. H. Linnard, "The Metric System in Shipbuilding," Transactions of the Society
of Naval Architects and Marine Engineers (New York, 1903), vol. ii. pp. 168-188.
CHAPTEE V.
THE METRIC SYSTEM OF TO-DAY—ITS ESSENTIAL CHAR-
ACTERISTICS AND FUNDAMENTAL PRINCIPLES.
The metric system to-day represents a complete, uniform, and
simple international system of weights and measures, and as such
may be considered briefly in its entirety, and with a view of the
relation of the various units to one another. In the beginning
it must be understood that any particular metric unit as such
does not possess any intrinsic superiority over other units, but
by reason of being united into a system which is strictly symme-
trical and systematized on one base ratio throughout, and with
that base ratio 10, metric units have many and preponderating
advantages over those of other systems. Nevertheless, bearing in
mind the two conditions mentioned, which are fundamental, there
is nothing to prevent other systems being constructed with other
units which would no doubt be equally satisfactory. But in reply
it may be said, Why should this be done, when a system exists,
used not only by men of science generally but by a large part of
the civilized world, the abandonment of which would surely accom-
plish no particular purpose. " For," says Professor R. H. Smith,1
" no other can possibly be better in practical essentials except in
substituting for ten the base twelve or thirty for measures and
written numeration alike, and this latter is humanly impossible."
For ordinary purposes of simple measurement, units are
grouped into five different classes, those pertaining to measures of
1 Professor R. H. Smith in Journal oj Institution of Electrical Engineers, quoted
by A. Siemens in Proceedings, Royal Statistical Society (London), p. 693, vol. lxvi.
1903.
\
136 EVOLUTION OF WEIGHTS AND MEASURES
length, surface, volume, capacity, and weight, or, as regards the
last, speaking more exactly and scientifically, mass. These all
depend upon the meter as the fundamental unit, and as a primary
and essential condition of the system, all must bear a strictly
decimal relation to each other. Inasmuch as in the metric
system all are referred to one primary standard, the Meter, there
must be necessarily absolute uniformity, and as means have been
taken to preserve this standard from any deterioration due to-
time or other causes, there is every guarantee of the stability of
the system and of its standards. Furthermore, what was once-
deemed desirable but found to be impossible of realization,,
namely, the definition of a standard by some object or circum-
stance in nature, has been accomplished, and to-day we have the
meter precisely defined in terms of the wave-length of cadmium
light by a method which is described elsewhere.1 Thus in the
event of the loss or the destruction of the International Prototype
Meter or of the copies thereof, it would be possible to reproduce
the exact length by experiments that to the practised physicist
involve no serious difficulty.
With the fundamental unit, the International Prototype Meter,
defined as the distance between two fine lines on a particular
platinum-iridium bar, at the temperature of melting ice, and
reproduced by national standards accurately copied therefrom and
duly recognized by the laws of the countries owning them, by
simply multiplying by ten successively or by a similar simple
process of decimal subdivision, is built up a system of measures
of length which have been demonstrated as sufficient for the
needs of science, commerce, and industry. Each unit is
either ten, one hundred, one thousand, ten thousand, or a million
times as great as the fundamental unit of length, the meter, or a
similar fraction or sub-fraction. This relation for many purposes
it is convenient to express by means of the number 10 and the
appropriate exponent or index, and then speak of a certain
number of meters multiplied by 10, 102, 103, 104, 106, or for the
sub-multiples 10"1, 10 ~2, 10" 3, etc. Consequently, in a number
expressing a length in a metric unit, it is possible to change the
unit merely by moving the decimal point or adding a requisite
number of zeros to correspond with the necessary decimal multi-
1 See chapter x. pp. 261-266.
THE METRIC SYSTEM OF TO-DAY 137
plication or division. Thus, as will be seen from the following
table, 1 kilometer may be written as 1000 meters simply by adding
three zeros to the 1, while 1 decimeter may be expressed in
terms of the meter simply by moving the decimal point one
place to the left. Taking fundamental units other than those of
length, which, however, are derived from the meter, a similar
method of decimal multiplication and subdivision enables us to
derive complete sets of units for surface, volume, capacity, and
mass measurements. For the first two we use the square meter
and the cubic meter as the fundamental units, and for capacity
the liter, and for mass the gram.
For the multiples of its principal units the metric system
employs prefixes derived from the G-reek as follows :
Deca meaning 10 times derived from Greek Seica. = 10
Hecto „ 100 „ „ €kclt6v= 100
Kilo „ 1000 „ „ x^a = 1000
Myria „ 10000 „ „ fwpia = 10000
Similarly, prefixes derived from the Latin are employed for the-
submultiples of the various units. These are as follows :
Deci meaning ^ derived from Latin decern = 10
Centi „ y^ „ „ centum = 100
Milli „ TJ}^U „ „ mille=1000
These seven prefixes always used in the same relation supply the
means of obtaining units of a size convenient for the work in
hand, and alway instantly available for conversion into units of
another denomination. To facilitate remembering the fact that
the Greek prefixes indicate multiples, and the Latin the sub-
multiples, one has merely to think of the word " Gild," and
understand that it stands for the initials of the motto, " Greek
increases, Latin decreases." With the three primary units, in-
volving the three names meter, liter, aud gram, and the two
more arbitrary units are and stere, together with the seven
prefixes given above, it is possible to construct all the metric
units in ordinary use, inasmuch as their relation to each other-
is perfectly uniform and simple.
138 EVOLUTION OF WEIGHTS AND MEASURES
Metric Measures of Length.
Unit.
Abbrevia-
tion.
Where Employed.
Value in Terms
of Meter.
Power
of 10.
Megameter, -
Astronomy
1,000,000m.
lO^m.
Myriameter,
Mm.
Geography
10,000m.
104m.
Kilometer, -
Km.
Distance
1,000m.
103m.
Hectometer,
Hm.
Artillery
100m.
102m.
Decameter, -
Dm.
Surveying
10m.
10m.
Meter,
m.
lm.
Decimeter, -
dm.
[Commerce
•lm.
lO^m.
Centimeter, -
cm.
-j Industry
•01m.
10"2m.
Millimeter, -
mm.
1 Science
•001m.
10"3m.
Micron = /*, -
(Metrology
•000,001m.
10~6m.
Millimicron,
■I Spectroscopy
[Microscopy
•000,000,001m.
10-9m.
While the foregoing represent the various units of length in
the metric system, and indicate the principal departments of
knowledge in which they are used, it does not follow that all of
them are used, or that a given length is expressed in terms
of more than one. For example, a distance is not expressed as
34 kilometers, 9 hectometers, 3 decameters, and 4 meters, but
as 34*934 kilometers, and all measures of length, where it is
desirable to use kilometers, are expressed in that unit and a
decimal fraction. Thus, for each class of measurements, as a
general rule, there is used but one of the above units, as will be
discussed below, and any measurement is expressed in whole
numbers and decimal fractions. Each of the above units is well
suited for a number of varieties of measurements, and a few of
these may be conveniently outlined. The megameter, which has
not received legal sanction, is but rarely encountered, and then only
in astronomical work where distances of considerable magnitude
are discussed. As it appears only in calculations it does not
possess much general interest, and the same holds true for the
myriameter formerly used in geographical work. The kilometer,
on the contrary, as a unit of distance such as would be used in
the measurement of the length of a railway or road, is of vast
THE METRIC SYSTEM OF TO-DAY 139
importance, and is universally employed both scientifically, as by
engineers, and also in non-technical matters. It is a unit whose
use presents very little difficulty to those accustomed to Anglo-
Saxon measures, in that it corresponds so closely to six-tenths of
a mile that such an approximation suffices for most purposes and
is readily made.
The hectometer does not find extensive practical application,
and is encountered chiefly in the calculations of artillerists ; but
even here it is preferable to use meters, and velocities, etc., are
now usually calculated in the latter units. The decameter is
used in surveying where it forms a base for the measure of land,
since the decameter squared gives the are, which is the principal
unit of land measure. The classes of measurement for which the
meter is available are numerous and apparent. For the measure
of cloth and similar fabrics it is eminently suitable, and as the
yard is approximately '9 of the meter there is no very violent
break in passing from one to the other, as would be done by
the purchaser of cloth for a dress. The meter would be used by
the stone mason in the measurements of a length of wall, or by a
carpenter or architect in his specifications and plans for structural
work, and is in every way as suitable a unit as the yard, aside
from the inherent merits of its connection with the metric
system. In the decimeter there is a unit intermediate between
the meter and the centimeter, and on that account not as much
used as either. Furthermore, the decimeter does not correspond
to any unit that has been in recent use by non-metric countries,
and in the Anglo-Saxon system its nearest equivalent is the hand
of four inches, long obsolete, except in measuring the height of
horses. The decimeter is too short to fill the place of the foot
and too long to supplant such a unit as the inch. Nevertheless,
it is at the disposal of those who desire such a unit, and as
three decimeters will approximate a foot, it may find increased
application, but its use has never been great in the countries
employing the metric system. The centimeter, on the other hand,
is a most useful and convenient unit, and is susceptible of wide
application. For the carpenter or cabinetmaker in giving the
dimensions of a door or window, the size of a plank, that is, its
breadth and thickness, or the dimensions of any ordinary objects,
such as tables, chairs, etc., the centimeter fills every requirement,
140 EVOLUTION OF WEIGHTS AND MEASURES
and in scientific work it is customary to express dimensions of
apparatus and all ordinary measurements in its terms. For
many years in the United States library catalogue cards and
other furnishings, such as pamphlet cases, have been standardized
and sold according to metric measure, and the centimeter has
been the unit adopted. It takes the place of the inch, and while
it requires a larger number to express a given distance, yet it is
likely to lead to greater exactness where it is not desirable to
employ fractions. The millimeter is the unit of science and
exact mechanical work. It affords an integral unit for minute
measures, speaking comparatively, and its decimal subdivision is
peculiarly suitable for this class of work. In ordinary life its
chief application is to the measurement of thickness, such as
metals, paper, glass, etc., and particularly in the measurement
of diameters of wire, tubing, and other materials which enter
into mechanical construction. Thus, measurements in millimeters
are designed to take the place of arbitrary gauges where the
problem of original standards, which in turn are based on
standards of length, works against general uniformity and con-
venience. For the measurement of screw-threads the millimeter
is also employed, and in France, Germany, and Switzerland
millimeter sizes for screws and thickness and diameters have
been found to be far more convenient than arbitrary gauges.
While the millimeter answers many purposes of the scientist,
yet it does not carry him far enough, and accordingly there is
the micron, which is one-thousandth part of it. This affords a
convenient unit for the microscopist and the spectroscopist when
they venture into the regions beyond the range of the human
eye ; and to secure a still greater refinement we have the
millimicron, or again the thousandth part.
With such units as the foregoing, the next point is how are
they applied, and how are they concretely represented by scales
or other devices ? The longest scale is that of the geodesist
or engineer employed in measuring his base line for trigono-
metrical surveying of greater or less accuracy as the occasion
may warrant. The best modern practice involves the use of a
steel tape or wire, or one made of an alloy of steel with a smaller
tendency to expand and contract with changes in temperature,
which under a constant tension gives an exact representation of
THE METRIC SYSTEM OF TO-DAY 141
a distance as determined with a standard of length.1 Such tapes
or wires are usually of 100, 200, or 300 meters, while the ordinary-
chain or tape of the land surveyor is either a double or single
decameter on which are marked the meters and such other
subdivisions as are desired, the double decameter being known as
a metric chain. The next measure of length in point of size
is the double meter, which may be either a rod or tape. If a
rod, its material and subdivision are dependent on the use for
which it is designed, as a metal scale lends itself more readily to
permanent and accurate graduation, and is less susceptible to
change with time and temperature ; the latter condition, in fact,
may be accurately and satisfactorily accounted for by knowing
the coefficient of expansion of the bar and the temperature at
which it is used. The tape may be either of metal or linen,
and is a convenient measure for many purposes. There are also
constructed meter scales, half-meter scales, double and single
decimeter scales, the shape and material as well as the accuracy
of graduation depending on the purposes for which they are to
be used. When it comes to the division of millimeters it is
necessary to employ a dividing engine,2 and the finest scales are
ruled on glass or upon a smooth and even substance, such as
speculum metal platinum-iridium, or nickel steel. The glass
scales are, of course, to be used with the microscope, and similar
scales can be constructed photographically by reducing in a
desired proportion.
1 There are also standard bars used in the most refined base measurements, such
as that at Holton, Mich., which was of 5 meters length. These bars require the
most careful levelling, are packed in ice at the time of making the measurement,
and are only used when the greatest accuracy is desired, as the refinements of a
laboratory are involved in a field operation. See Woodward, "The iced bar and
long tape base apparatus and the results of measures made with them on the
Holton and St. Albans bases," part ii. of Appendix No. 8 of Report of United
States Coast and Geodetic Survey for 1892, pp. 334-489. Professor Woodward
also discusses "Long Steel Tapes" in a paper presented to the International
Engineering Congress of 1893, and printed in the Transactions of the American
Society of Civil Engineers, vol. xxx. p. 81.
2 See chapter x. — Standards and Comparison, p. 225.
142 EVOLUTION OF WEIGHTS AND MEASURES
Number of Square
Abbreviation.
Meters.
km2.
1,000,000m2.
ha. — hm2.
10,000m2.
a. — dm2.
100m2.
ca. or m2.
lm2.
dm2.
•01m2.
cm2.
•0001m2.
mm2.
•000,001m2.
Measures of Surface.
Square kilometer,
Hectar (square hectometer),
Ar (square decameter), -
Centiar or square meter,
Square decimeter,
Square centimeter,
Square millimeter,
For the measurement of surfaces it is customary to employ
as a unit a square or quadrilateral figure bounded by four equal
sides at right angles to each other. In such a unit the sides are
usually made equal to the linear unit, hence in the metric system
a square of this nature would have for each side a meter, and
would be known as a square meter, forming the principal unit
for the measurement of surface. The next greater unit would be
formed by a square whose bounding sides were each equal to a
decameter, and consequently would include 100 of the principal
units. If our units of length increase by a ratio of 10, it is
obvious that the unit of surface based on these same units of
length must increase by the square of 10 or by 100 as is indicated
by the table. The same nomenclature is retained, but the word
square is prefixed, and in the case of the units formally adopted
for the measure of land, the terms hectar and ar have been
selected to designate respectively the square hectometer and the
square decameter. In writing and converting the measures of
area it is necessary to multiply or divide by 100 when changing
to a larger or smaller unit, consequently in the decimal fraction
each metric unit must be given two places of figures. For
example, to write as square meters 984*8963 square decimeters, it
would be necessary to move the point two places to the left and
we would have 9*848963 square meters, which also could be
written 9 square meters, 84 square decimeters, 89 square centi-
meters and 63 square millimeters, or even 9848963 square milli-
meters if it was so desired. The square kilometer is employed
in topographical work on a large scale, or in cartography in
summing up the area of a country or large region. For fields
THE METRIC SYSTEM OF TO-DAY 143
the hectar is used, and is parallel to the acre, which contains
•4047 hectars. For land of smaller dimension, such as city lots,
it is customary to use the are. The measurement of surfaces, as
of walls by the painter or paperhanger, or of floors by the dealer
in carpets, is naturally made by the square meter. Such measure-
ments as the square decimeter and the square centimeter are
useful for purposes that will naturally suggest themselves, but
again attention may be called to the fact that scientific men
prefer to use the square centimeter and the cubic centimeter
also as much as possible.
Measures of Volume.
The volume of a body, or the amount of space that it occupies,
is usually measured by a unit known as a cube, which is a
parallelopipedon bounded by six equal squares. In the metric
system the principal unit is the cubic meter, a cube each of
whose faces is a square meter, and consequently whose edges are
each a meter in length. The cubic meter is the largest unit of
volume in the metric system, though logically there is no reason
why cubic decameters, hectometers, and kilometers should not be
employed were there any necessity for their use, which there is
not. Therefore we have only to concern ourselves with the sub-
multiples of the cubic meter. On the decimal principle the
next smaller unit must be one in which the size is determined
by the tenth of the meter, or the decimeter, or a cube each of
whose edges is a decimeter. Obviously, to make a cubic meter
ten rows of these cubes, arranged so that they are ten in
length, will have to be placed ten deep, or one thousand of our
cubic decimeters must be used. So that where the unit of area
required a ratio of 100 to pass from a smaller to a greater, the
units of volume need a ratio of 1000 ; that is, three figures of
integers or of the decimal fraction are required for each unit.
Thus a cubic meter will contain 1000 cubic decimeters, or
1 000 000 cubic centimeters, or 1 000 000 000 cubic millimeters.
We may read 76'854 673 2 cubic meters as 76 854*673 cubic
centimeters, or, were it desirable, 76 854 673 cubic millimeters.
Or we could read the above expression as 76 cubic meters,
854 cubic decimeters, and 673 cubic centimeters.
I
144 EVOLUTION OF WEIGHTS AND MEASURES
The cubic meter is employed in all cases where any con-
siderable quantity of a substance must be considered. Thus
the amount of material excavated from a foundation, railway
cut, or canal, would be expressed in cubic meters, as would be
blocks of marble or the contents of a tank or reservoir. When
the cubic meter is applied to the measurement of firewood it
receives a new name, stere ( = 35*317 cubic feet or *27 cord), and
as a pile of wood can be divided or increased readily, the name
of decistere is given to the one-tenth part, and that of decastere to
ten times the unit quantity. The cubic decimeter is an inter-
mediate unit like the corresponding decimeter and square
decimeter, but it possesses importance, inasmuch as it is the
volume of the liter (very nearly), and as such is frequently
employed in calculations where it is desired to obtain the
capacity of a given space, as will be explained further on under
measures of capacity. The cubic centimeter answers for many
purposes, and is the usual unit for scientific work. Thus in
pharmacy by the volumetric method (see page 194) almost all
liquids are compounded by taking the desired quantities in cubic
centimeters, while to determine standard pressure reference is
made to that of a column of 75 cubic centimeters of mercury at
0° centigrade.
Measures of Capacity.
Hectoliter, -
Decaliter, -
Liter, -
Deciliter, -
Centiliter, -
Milliliter, - ml. -001 liter.
The close connection between measures of volume and capacity
is obvious, and the founders of the metric system took as their
unit of capacity the volume of a cubic decimeter. Subsequent
measures of the kilogram, and the mass of water necessary to
amount to this weight, resulted in the conclusion that for strictly
scientific purposes this was inaccurate, and consequently the legal
definition is in the words of the International Committee, " The
liter is the volume occupied by the mass one kilogram of pure
hi.
100 liters.
dal.
1.
dl.
10 liters.
•1 liter.
cl.
•01 liter.
THE METRIC SYSTEM OF TO-DAY 145
water at its maximum density and under normal atmospheric
pressure," and this decision was duly sanctioned by the general
conference of 1901. As the result of a large number of careful
experiments it was found that a mean value for the mass of a
cubic decimeter of water at 4 degrees centigrade (its temperature
of maximum density) would be '999974 kilogram, and that the
error of assuming the liter equal to the cubic decimeter would be
only about one part in 30,000, an amount only appreciable in the
most refined measurements. The liter is subdivided on a
decimal basis, while its multiples are similarly arranged, and
from what has preceded it will be possible to understand the
various units merely by referring to the table. In actual practice
the liter and the hectoliter are the units chiefly employed, as for
many reasons it is preferable to employ cubic centimeters for
smaller measures, while the decaliter, being an intermediate
measure, does not come into wide use. The liter and all the
measures of capacity are used for both dry and liquid substances ;
but it is a tendency of modern metrology quite independent of
the metric system to do away so far as possible with dry
measures of capacity and buy and sell such substances by weight.1
^ The liter, however, can be used to measure all liquids (such as
water, milk, wine, beer, oil, etc.), vegetables, grains, seeds, etc., in
ordinary retail transactions. When large quantities of the
commodity are dealt in or discussed, then it is customary to use
hectoliters. The liter corresponded so closely to the ancient
French pinte ('981 liter) which it supplanted that its use did not
occasion any difficulty, and as it is intermediate in value between
the American dry ( = 1*1012 liter) and liquid quarts ( = '94636
liter) its employment would result in a simplification of measures,
and would involve no inconvenience.
The adoption of metric measures of capacity in the United
States would result in important simplifications, as the present
measures differ from those of Great Britain, and possess no
intrinsic merits of their own. In fact, in the Anti-metric
Argument of the Committee of the American Society of Mechanical
Engineers (vol. xxiv. New York, 1902), which opposes most
bitterly any attempt at the introduction of the metric system, it
is stated (p. 676), " That there is no reason for the English
1 In Europe the practice of selling liquids by weight is also increasing.
K
\
146 EVOLUTION OF WEIGHTS AND MEASURES
.z
system retaining the gallon and the bushel except that they are
in such common use. For convenience in computation it would
be well if the gallon were 216 cubic inches, or the cube of 6
inches, and the bushel 1728 cubic inches, or 1 cubic foot."
In constructing the actual measures of capacity their range is
extended by binary subdivision and doubling, so that all possible
capacities can be measured and substances sold on a basis of the
simplest mental process, namely, that of halving. Actual measures
in the form of wooden vessels for measuring grain with a capacity
of one hectoliter and less are constructed with their internal
height and diameter equal, while for measuring liquors, wines,
and alcohol, the French laws provide that the internal height
should be twice the internal diameter. Oil and milk measures
are of tin, and their internal height and diameter are equal.
Measures of Mass.
Metric ton,
t.
10 Quintals
1000 Kilogran
as 1,000,000
grains
io6g.
Quintal,
q-
10 Myriagrams
100
100,000
n
10%.
Myriagram,
10 Kilograms
10
10,000
i
10*g.
Kilogram,
kg.
10 Hectograms
—
1,000
)i
io3g.
Hectogram,
10 Decagrams
—
100
i
io2g.
Decagram,
10 Grams
—
10
i
lOg.
Gram,
g-
10 Decigrams
—
1
i
E-
Decigram,
dg.
10 Centigrams
—
•1
,
io-ig
Centigram,
eg.
10 Milligrams
—
•01
i
io-V
Milligram,
mg
—
—
•001
i
10"3g.
V
By mass is meant the actual quantity of matter which a body
contains, and it is to be distinguished from weight, which is the
force with which a body is attracted to the earth. Now, as this
force of attraction depends upon the mass of a body, it follows
that the weight of different bodies at the same place is pro-
portional to their respective masses. But as the force of
attraction or gravity varies at different points on the earth's
surface, it is obvious that bodies of the same mass will have
different weights at different places. Originally, as we have
seen, the gram was defined by the decree of 18 Germinal, year
III.,1 as " The absolute weight of a volume of pure water equal to
a cube of the one-hundredth part of a meter and at the temperature
1 See p. 54.
THE METRIC SYSTEM OF TO-DAY 147
of melting ice," and on this basis the Kilogram of the Archives
was constructed. However, after the construction of the Inter-
national standard kilogram it was deemed desirable to define
formally the kilogram, and at a meeting of the International
Committee on October 15, 1889, it was decided that "The mass
of the international kilogram is taken as unity for the inter-
national system of weights and measures," and this decision was
confirmed at the third general conference held at Paris in 1901.
While the gram is the fundamental unit of mass, yet in actual
practice, as in the construction of the standard, it has been found
rather small for most weighings, and consequently the kilogram
is employed as a practical unit.
There is, of course, the same wide range of units of weights as
in other classes of measures, and on precisely the same decimal
basis, as the table plainly sets forth. The same considerations
govern their use, and we find that the number of units in actual
use is but a small part of those available. Thus, for large
weights the metric ton is the unit employed, and is used in the
weighing of ore, coal, hay, and other substances dealt in in
large quantities. It is employed in estimating the mineral pro-
duction of the world, being a convenient weight to which the
output of different nations may best be reduced for purposes of
comparison and statistical study. It corresponds so closely with
the long ton of 2240 pounds (a metric ton equals 2204*62 lbs.)
that for many purposes it is practically equivalent. The quintal
has the same line of uses as the hundredweight, which either
as 112 pounds or 100 pounds is still employed in some branches
of trade. It would be substantially equivalent to twice the
former, and would not vary greatly from the American barrel of
flour, which contains 196 pounds net. /
The myriagram is rarely, if ever, used, but the kilogram is a
unit which is found universally. Being the weight of a cubic
decimeter of water it enables one instantly to determine the
weight of a body whose volume and specific gravity are known, «/
and for that reason is very convenient in calculation, such as to
determine the weight of cut stone, etc. It is the unit most
frequently employed in trade and industry for the sale of
merchandise of all descriptions. By using the half kilogram
there is a weight which approximates the pound, and being
148 EVOLUTION OF WEIGHTS AND MEASURES
slightly larger there is an element in favor of the purchaser.
Instead of using hectograms and decagrams it is found more
convenient to express such quantities in terms of fractions of
kilograms or as grams, and such is the usual practice. The gram
is extensively employed in science, as by the chemist, and by
those dealing in small and valuable materials, as jewellers and
coiners. In multiples of ten it affords a convenient substitute
for the ounce, 30 grams (28*3495 exactly) corresponding to one
ounce avoirdupois. Its relation to the cubic centimeter of water
makes it a useful unit for the physicist or chemist, and unless
there is reason to the contrary it is always used to record and
describe the results of his experimental and other work. As the
gram is so constantly used for measures of weight of this nature
by those having to do with masses of a size convenient for its
use the adoption of this part of the metric system would work no
hardship, as apothecaries' weight, which it would supplant, has few
defenders, and is destined to disappear: Decigrams, centigrams,
and milligrams are used in the form of fractions of the gram,
though milligrams are employed to a certain extent, especially as
the riders or smallest weights of a fine balance enable weighings
to be made in milligrams and fractions of a milligram.
In the actual weights there is not only the diversity indicated
by the table, but also others obtained by doubling or halving the
various units there mentioned. The construction and design of
these weights as also their accuracy depends upon the purpose
for which they are intended, and vary from the platinum iridium
and rock crystal copies of the international standard down to the
cast-iron weights of the retail dealer. The cast-iron weights
range from 50 kilograms to 50 grams or J hectogram, while the
brass weights, which are usually cylindrical in shape, with the
upper part fashioned into a knob for more convenient handling,
range from 20 kilograms to 1 gram. Fractions of a gram are
usually made of sheet metal, such as platinum, german silver, or
aluminium, as in this shape they are more readily handled with
the forceps employed to transfer them from their case to the
pans of the balance. The very smallest or milligram weights are
known as " riders," and are twisted loops of wire which may be
placed at any desired position along the graduated beam of the
balance, and thus enable the observer to read to fractions.
THE METRIC SYSTEM OF TO-DAY 149
While there have been enumerated under each class of
measures a number of units, yet it is necessary to state again that
only a comparatively small number are employed. In this
respect the metric system is similar to the United States
monetary system, where there are mills, dimes, and eagles, as well
as quarters and halves, in addition to dollars and cents, but in
computation everything settles down to a dollars and cents basis.
This is precisely the case with the metric system, and while the
intermediate units appear in the tables we have taken care to
explain how infrequently they are employed. In fact, it is a
tendency in metrology to eliminate from use as many units as
possible, and all existing measures are on a far less liberal scale
in point of numbers than those of a century ago, not to speak of
those of ancient times or of the middle ages. With the metric
system this elimination can be done without any trouble, as it is
the work of but a moment to change from one unit to another
for any purpose whatsoever.
CHAPTEE VI.
THE METRIC SYSTEM FOR COMMERCE.
Feom what has been said regarding the development and present
conditions of the metric system, the advantages of its use by
all nations would seem apparent ; nevertheless, as its employ-
ment is not as yet universal, it would seem desirable here to
deal first with the benefits to the commercial world at large of
a single system of weights and measures, and second with the
profit that would accrue to an individual nation from the adop-
tion of the metric system. It is a mere truism to say that
anything that enlarges the circle of exchange of either ideas or
commodities works for the welfare of the world, and the happiest
and most prosperous nations are those that have the advantages
of such interchange with their fellows most firmly established.
A striking example of this is seen when it is considered that
the improvements in navigation following the application of steam
have not redounded to the benefit of any one nation to the
exclusion of others, but have stimulated trade and prosperity in
all parts of the world. Likewise by means of the telegraph and
submarine cable the exchange of ideas and rapid transaction of
business between distant places have been made possible, and that
again has brought about benefits confined to no single nation.
Furthermore, international banking has also contributed to extend
and develop trade, and here we find that through the pre-eminence
of Great Britain in this field pounds sterling are adopted as a
universal measure of value. Facilities have been supplied by
the British merchant and banker which have resulted in no
small profit to him, simply because he has been able to occupy
the world with his commercial machinery and force the use of a
standard of value adequate for a large part of the world's trade.
THE METRIC SYSTEM FOR COMMERCE 151
On the other hand, a result of international co-operation is the
International Postal Union, where mails from all countries of
the world are exchanged with equal and proportionate expense
and advantage to all. Here, as we have seen,1 it was necessary
at the outset to find a common system of weights and measures
to regulate the payments and the exchanges of mail, and it was
found desirable to adopt the metric system, which has since been
employed for many years with complete success even among
non-metric nations. In general, wherever there has been inter-
national co-operation to secure uniformity in commerce, as in
cable and telegraph conventions, treaties to establish uniform
classifications and definitions, etc., the results have invariably
resulted in promoting general prosperity and in increasing
business. Furthermore, an international language, as well as
an international currency, would serve to increase commerce and
from many points of view would be an important benefit.
However, international language and international currency are
outside the province of the present consideration, but inter-
national weights and measures must be discussed, especially as
the metric system is destined eventually to hold such a position,
even in a fuller sense than at present. The reasons for this
present pre-eminence, as we shall soon see, are obvious. First,
in different contiguous countries, there was the realization of a
need of a single system of measures that would conform to those
of the other nations ; and second, there was the natural desire
for the best and most useful system. The result was that in
every instance where a change was made, save that of Russia2 in
1835, the metric weights and measures were adopted in preference
to those of any other system, and in no case have they been
given up, nor is the slightest desire for any change expressed.3
For the benefits of a single and international system of units,
we have only to refer in passing to the electrical units which
are subsequently discussed at some length,4 For the measure-
ment of electrical quantities throughout the world a single system
1 See ante, p. 127.
2 Russia adopted as a unit of length 7 English feet, but neither multiples or
submultiples were as in the British system. Furthermore the British pound was
not adopted.
3 See chapter iii. ante. 4 See chapter ix.
152 EVOLUTION OF WEIGHTS AND MEASURES
of units is employed, and this system, based on the metric
units, was developed in Great Britain, and has been adopted by
scientists and engineers universally. When great industries
were established to apply to the everyday uses of mankind the
discoveries and inventions of men of science in this field, these
same units were retained, and were later sanctioned by inter-
national agreements. No voice has ever been heard to dispute
the advantages of such a system, and the result has been that
there has been more progress in electricity through the inter-
change of ideas than in any other branch of applied science.
When electrical congresses meet every communication is in-
telligible at once to every member so far as the expression
of quantities goes. When tenders are asked for electrical
machinery, materials, or apparatus, the manufacturers of every
nation of the world are on the same footing as regards under-
standing the specifications and utilizing materials for a desired
output. Accuracy in measurement is not restricted to any
single nation or its scientific workers, as the work of the latter
can be put immediately at the disposal of the world, and the
highest precision can be secured by joint effort and co-operation.
In fact, when the Physicalisch-Technische Keichsanstalt at Char-
lottenburg, near Berlin, was the only important governmental
testing bureau and physical laboratory, it received apparatus and
materials from many nations outside of Germany to be examined
and standardized according to the common system. To-day elec-
trical measuring instruments certified to by the Keichsanstalt, the
Laboratoire Central d'Electricite* at Paris, the National Physical
Laboratory of England, or the U.S. Bureau of Standards, can be
used for electrical measurements anywhere in the world, as the
units employed depend for their derivation on the same defini-
tions. In fact, so much a matter of course is the single system
of electrical units that no one would think of proposing any other,
and its existence is so taken for granted that its advantages are
rarely spoken of or even considered until the possible chaos of sub-
stituting a number of systems in its place is mentioned. Indeed,
while the various units are frequently criticized, no electrician
or physicist would venture to propose the adoption of new units
locally, despite the fact that universal reforms in units and
standards are advocated before international congresses.
THE METRIC SYSTEM FOR COMMERCE 15S
Looking at the question of weights and measures from a
strictly commercial standpoint it is clear that, as commerce
involves primarily the exchange of quantities of various com-
modities, the use of a simple and convenient method for the
rapid calculation of weight, length, and capacity must promote
ease and security of commercial intercourse. The metric system
being decimal, and consequently the most easily grasped and
applied, is therefore the best for commerce, and when to this
is coupled the fact that its use is all but universal and is em-
ployed in the major portion of international commercial trans-
actions, it is easy to see that a great saving of time in business
operations must result from its adoption. That this saving of
time and simplicity is real, and not the mere hope or opinions
of reformers, can be demonstrated by reference to the reports of
American and British consular and diplomatic officials who are
acquainted with both the Anglo-Saxon and the metric systems.
These reports, notable among which, as being most comprehen-
sive and complete, are those presented to Parliament in 1900'
and 1901,1 to which reference has already been made, speak
emphatically in this respect, and in a communication from
Portugal appears the statement that " The large amount of time
saved in commercial houses by the simplicity of the metric
system, as well as by the uniformity now existing in place of
the former chaos, is in itself a valuable factor in considering
the advantages of the new system." 2
The successful prosecution of foreign commerce requires a
complete understanding between merchants in different countries
as to each other's standing, methods of payment, and, most
important, as to the goods themselves which form the subject of
the transaction. Aside from standards of quality, quantities and
dimensions must be considered, and it is here that universal
measures and standards are needed. It is also of importance for
both buyer and seller to know the quantity of the commodity in
existence at different places, the quantity produced and consumed
in previous years, and other statistical information. As regards
1 English Parliamentary Accounts and Papers: 1900, vol. xc. ; Reports from Her
Majesty's Representatives in Europe on the Metric System: 1901, vol. lxxx. ;.
Reports on Metric System, part ii.
2 Ibid, part i. p. 54.
154 EVOLUTION OF WEIGHTS AND MEASURES
the latter, it will readily be seen that the collection and diffusion
of such knowledge would be facilitated if the same units were
used in every country and port of the globe, and trade could then
be carried on in a more intelligent manner, and with the elimina-
tion of speculative elements, while tariff laws and custom regula-
tions, etc., could be more intelligently framed through the better
and more uniform character of the statistical information. Such
benefits accrue to trade throughout the world generally, and are
generally recognized.
But with no uniform system of weights and measures which
may be applied to the description of goods, it is inevitable that
there is a lack of clear understanding between buyer and seller,
and one of these parties is at a disadvantage. Especially is this
true if there is a competitor who is ready to trade on a basis more
readily understood. Thus, if a man is in doubt as to certain
elements concerning goods which he desires to buy or sell, he
naturally assumes that there are other points about which he is
equally ignorant, and consequently he is unwilling to undertake
the transaction. True, he may compute in his own system the
quantities or dimensions of the article or articles, or may receive
these figures in whole or in part from the other merchant or
agent ; but the basis of trade is unsatisfactory, and it is natural
for men to buy or sell according to their usual measurements even
if the goods must be imported from a greater distance. This,
furthermore, is emphasized by the extensive use of standards
which, at first designed for a single country and trade, have
gradually crept abroad so that if either English or Continental
goods, such as pipe or nuts and bolts, for example, have secured
a foothold in a certain country, it is quite certain that in all
subsequent orders they will be demanded, and a newcomer in the
field will have to conform to styles and standards already estab-
lished. Thus to compel trade in a large and unusual number of
sizes is a most wasteful economic process, and results in forcing
the manufacture into the hands of a comparatively small number
of producers, who can so control their business as to occupy
certain fields exclusively rather than to establish wholesome
competition between all the manufacturers of the world.
A striking example of the evils attending lack of standardiza-
tion in measures, materials, and machinery, is to be found in
THE METRIC SYSTEM FOR COMMERCE 155
the mining districts of South Africa, where mining and other
engineering operations are carried on in a cosmopolitan manner
by engineers from various countries. Machinery and supplies are
imported, for specific purposes, from all over the world, and con-
sequently they vary in dimensions, often in parts that properly
should be interchangeable.1 The result is that considerable fitting
is required in order to make the various parts of a plant work
harmoniously. This of course involves time and expense without
accompanying benefit to anyone, whereas by a system of inter-
national standards such waste would be avoided. Furthermore,
a proper system of standardization would enable the specifications
of machinery and supplies to be prepared in such a way that
manufacturers and dealers would know exactly what was wanted,
and make their bids accordingly, to the benefit of all concerned.
If the standardization was universal a simple description of the
desired articles could be circulated, and manufacturers and dealers
all over the world could submit prices and estimates. Thus the
whole world could participate in the competition, and not only
would the supplies be cheaper to the purchaser, but manufacturing
and commerce would be stimulated.
Now, the first principle of standardization is the defining of
sizes in a regular and systematic manner, and conforming to a
permanent standard, and this in the ultimate analysis must
depend on a standard of length or mass. Consequently, if the
dimensions of articles are referred to one and the same system,
and that the international or metric system, it is comparatively
simple to reach a point where all articles of a class are reduced to
certain sizes determined by conference and mutual consent of the
makers and consumers of the commodities in question. There is,
in short, a survival of the fittest and most convenient sizes, and
machinery and materials, involved in making the various articles,
are soon conformed to these standards of size.2 It will be seen,
therefore, that the standardization which is a benefit, national or
international in accordance with its scope, follows from a well-
defined system of units, and when such a system is single and
1 See Presidential Address of R. M. Catlin before Mechanical Engineers'
Association of the Witwatersrand, abstracted in Engineering and Mining Journal
<New York), vol. lxxix. 1905.
2 See p. 173, chap. vii.
156 EVOLUTION OF WEIGHTS AND MEASURES
universal there is bound to result a single set of standards in all
important industries. Such a result is bound to promote com-
merce and industry by facilitating the manufacture and exchange
of commodities, and the same benefits would be experienced by
the world at large as have been realized in the United States
where this policy has been followed in many lines.
International weights and measures soon would produce truly
international standards, both of size and of quality, and the trade
of the world would be on a far more wholesome and active basis,
as there would not be material tied up in odd sizes, and con-
sequently unavailable to other users except at increased expense,
but there would be a common world stock. As trade would be
stimulated and diversified a further division of labor would take
place, and there would be greater general prosperity. To become
thoroughly convinced of this, one has only to refer to the reports of
American and British consuls, which are unanimous and constant
in reiterating the assertion that the lack of an international
system of weights and measures acts most strongly against the
extension of trade between their home countries in those places
in which they serve. This, of course, implies a reciprocal loss, as
the wider the distribution of a nation's commerce the more
extensive it must be, as also the more profitable.
That there is need of an international system of weights and
measures which is universal and invariable is shown by the fact
that the United States and Great Britain, which claim the same
sources for their various weights and measures, now have units
that figure constantly in trade relations which are quite unlike in
value. For example, wheat and other grain from America is sold
by a bushel which differs materially from the British bushel, as
does also the gallon used in the measurement of petroleum, while
the hundredweight of 112 pounds and quarter of 56 pounds are
rarely used in America. These weights were abandoned in
Liverpool in 1903 for a weight of 50 pounds, the use of which in
trade was authorized by an Order in Council of October 9, 1903.
Since that time a standard for this amount has been constructed
and verified, and there is an increasing tendency towards using
the cental of 100 lbs. as a commercial unit. Here are examples
of the inconvenience where two countries employ measures and
weights apparently the same, but which must be adjusted even for
THE METRIC SYSTEM FOR COMMERCE 157
transactions between themselves, when by the adoption and use of
the metric system they would be put on the same basis as regards
one another as they would enjoy towards the rest of the world.
Foreign commerce presents many difficulties unknown to
business between two parties in more or less proximity. There
is the question of time and of freight, both important items in
any commercial transaction, but especially so when weeks or
months must elapse before a delivery can be effected. Misunder-
standings or mistakes are most costly and cannot be rectified
promptly ; consequently there should be the most complete
understanding between the parties to the transaction. This must
involve an easy standard or basis of comparison, for the present
differences in money and exchange are troublesome enough. The
extent of this difficulty is best illustrated by modern methods of
doing business where catalogues, price-lists, and other printed
matter are used so extensively, and are such an important adjunct
to the work of the salesman, who naturally is unable to carry
with him a complete line of samples, even of agricultural tools,
not to mention dynamos and steam engines. If these descriptions
and prices are understood, and if the sellers have a good
reputation, much has been done towards effecting a sale, as the
prospective buyer can tell at a glance whether character, quality,
and size are such as he desires and uses, and especially whether
they will correspond in size with present or future stock or plant.
Furthermore, in case of an immediate demand for the goods,
business can be transacted satisfactorily by cable or telegraph.
When, however, various articles are presented to a foreign pur-
chaser described in strange units, the latter is compelled to
employ conversion tables, and even then fails at a complete, not
to speak of quick, comprehension of the goods. With a single
system the case would be different, and no nation would enjoy
any advantage over another in this respect, save in the actual
merit of its goods, and the increased circulation and use of such
•catalogues would provoke keener competition, and would result
in a higher grade of tools and other articles, as the world markets
would be aimed at where general excellence and price would
carry the day.
The question whether a country's export business would be
helped by an international system of weights and measures must
158 EVOLUTION OF WEIGHTS AND MEASURES
be considered, no matter whether that country is on a protection
basis or enjoys free trade. In the latter case the advantages are
obvious, but where there has been protection the result in many
nations is that the product is often greater than the needs of the
home market, consequently the manufacturer, in order to keep up
his production on the largest, and therefore most economical
scale, must seek to market his surplus in a foreign field. A
glance at our table (page 105) will soon show that with the
exception of Great Britain and its dependencies, Eussia, Denmark,
and China, the vast majority of nations are on the metric basis,
and for reasons we have already advanced it is quite necessary
that business with them should be done according to the inter-
national measures. That this is essential is shown by the fact
that in the United States certain manufacturers, and the number
is constantly increasing, not only describe their goods in metric
measures, but so construct them, and stand ready to increase
their business in this respect. If the surplus product is made so
that it can be utilized in any country, it is of course obvious that
the manufacturer has a far wider range of market, and is likely
to secure better prices.
Possibly the best testimony as to the advantages to commerce
of an international system of weights and measures should come
from countries where the metric system has supplanted the local
system or systems, though the latter still survive. Such is the
following extract, which sums up the conditions in Spain, and
which is typical of the enlightened opinion in nearly all metric
countries : " The facility and security afforded to the sending of
orders, owing to the amount ordered being subject to the same
measure in the different countries, the conformity in transport,
custom-house, and commission tariff, etc., attract, tighten, increase
commercial relations." 1 This is the answer of the Spanish
Geographical and Statistical Institute attached to the ministry of
Public Instruction, Agriculture, Industry, and Public Works, in
reply to a question as to how the adoption of the metric system
had affected its commerce, and it is also the experience of other
countries. The importance of the adoption of the metric system
1 Report of Her Majesty's Representatives in Europe on the Metric System, pre-
sented July, 1900, part i. p. 61 ; Parliamentary Accounts and Papers, 1900,
vol. xc.
THE METRIC SYSTEM FOR COMMERCE 15£
to international trade has been noted formally by various com-
mercial and statistical conferences and conventions, but of a more
official character was the action taken by the International
American Conference which was held at Washington in 1890,
where the following resolution was adopted : " Resolved that the
International American Conference recommends the adoption of
the metrical decimal system to the nations here represented
which have not already adopted it." James G. Blaine, then
Secretary of State, whose last important official work was towards
the extension of American commerce through reciprocity treaties
with the South American countries, urged upon the United States
Government the adoption of that system for the customs service,1
and his recommendations were concurred in by Secretary of the
Treasury Windom (Report, Dec. 1, 1890), and by Secretary of
State Foster, in his reports for 1891 and 1892. Likewise, in
Great Britain there was a conference of Colonial Premiers at
London in 1902, and a resolution was formally adopted favoring
the use of the metric system for all the British colonies. Fol-
lowing up the matter the Colonial Office then communicated with
the various Colonial governors, asking what action was likely to
be taken with regard to this resolution. Mauritius and
Seychelles already used the system, but the following colonies
were reported as favorable to its adoption : Australia, New
Zealand,2 Cape of Good Hope, Transvaal, Orange River Colony,
Southern Rhodesia, Gambia, Northern Nigeria, Gibraltar, British
Guiana, Trinidad, Leeward Islands and Windward Islands.
Sierra Leone, Southern Nigeria, Ceylon, and the Falklands
stipulated that they were in favor of it if adopted by the United
Kingdom or in the Empire generally. The Australian states,
while favorably disposed, thought that the matter should be
settled by the government of the commonwealth, while Jamaica
and British Honduras required the adoption of the system by the
United States. Fiji and British New Guinea would have to
follow Australia, just as the Straits Settlements and Labuan were
dependent on India. The Bechuanaland Protectorate would be
compelled to be in harmony with the rest of South Africa.
Opposition to the plans was evinced by St. Helena, Cyprus, Lagos,
1 Sen. Exec. Doc, No. 181, 51st Congress, 1st Session.
2 Metric System adopted by New Zealand in 1905.
160 EVOLUTION OF WEIGHTS AND MEASURES
Wei-hai-wei, Barbados, and Bahamas, while the Gold Coast
Colony and the State of Queensland were ready for the system,
but anticipated inconvenience in its adoption. Natal reported
that some definite general plan was necessary before an opinion
could be expressed. Of the remaining colonies definite answers
were not given by Newfoundland, Malta, or Bermuda, and no
reply whatsoever was received from Canada, though it is
sufficiently obvious that the latter country would be compelled to
follow the example of the United States.
It will be seen from the foregoing that these colonies, widely
scattered over the world, were for the most part alive to the
-advantages attending the adoption of the metric system, as by so
doing the great trade of the British Empire would then be put
on the same terms as that of the rest of the world. This, of
course, leaves out of consideration the trade of the United States
■and its possessions, which, if brought into harmony with the
above, would greatly facilitate in the development and prosecution
of commerce.
An additional consideration is that new discoveries of mineral
wealth and supplies of raw materials of one class or other have
within comparatively few years greatly extended the range of
commerce, and many nations once thought uncivilized and un-
productive are becoming great consumers as well as producers,
requiring the most varied supplies and machinery. These
markets are destined to prove among the most valuable of the
world, and to pre-empt them is the task of the highest wisdom.
In South America and in all non-British colonies we find the
metric system used, though with it are often various native or
local nondescript units. It is the opinion of the consuls to these
places — and they at least must be admitted to be competent
judges — that the use of the metric system would greatly increase
trade of these countries with America and Great Britain.
Having pointed out that the adoption of a single system of
weights and measures throughout the world would be most
advantageous, and would facilitate commerce, therefore benefiting
each and every nation to a greater or less extent depending on
its location and the amount of its foreign trade, it is now
necessary to consider just what advantages a country not using
the metric system would secure by its adoption, and what dis-
THE METRIC SYSTEM FOR COMMERCE 161
advantages, if any, are likely to be experienced. These advantages
must be practical, especially in a country like the United States,
and must appeal to the small shopkeeper and farmer, as well as
to the professor of physics, the merchant, and the statistician.
Large, as the question seems, it is possible to simplify it by
eliminating a certain number of elements. Thus, we know that
workers in science in America, Great Britain, and Russia have,
for a long time, universally employed metric weights and measures
in their daily work, and have urged their adoption for general
use, confident of their great utility and superiority. Also, that
other scientific men, whose work is of a more practical nature,
such as electrical engineers, who constantly use the metric
weights and measures in their work, have also urged their general
adoption. Consequently, the change would be a distinct advan-
tage to workers in this field, and there is no opposition to the
step to be anticipated from them.
At the other end of the scale must be considered the average
citizen who does business on a small scale, and who, with his
household, uses weights and measures daily. In fact, looking at
the question as a national one, this seems to be the most
important aspect, and should be most carefully considered, both
in the light of the experience of foreign countries and according
to local conditions. Reflection, however, soon establishes the
fact that most of these transactions take place where the actual
goods are transferred in the presence of the buyer and seller, and
some approximate idea of the measure desired is in the mind of
both of the parties to the transaction. Thus a man buying sugar
sees the amount he is receiving, and knows the price paid, so
that with properly sealed weights there is no opportunity for
injustice, as the man is free to buy sugar where he will, and at
the most favorable price, the latter being governed by the law of
supply and demand as modified by trade conditions. When his
wife mixes the sugar to make cake her methods of measurement
are purely relative, and neither ounces nor grams are employed,
but approximate measures, such as tea-cups, which are quite
independent of any laws of metrology. In fact, the question has
been excellently summed up by one of the most distinguished
opponents 1 of the introduction of the metric system into the
1 Dr. Coleman Sellers, Cassier's Magazine, vol. xvii. p. 365, 1900.
L
162 EVOLUTION OF WEIGHTS AND MEASURES
United States, as follows : " To the great bulk of mankind engaged
in trade, in buying and selling, in bartering and exchanging, it
matters little what system of weights and measures they adopt :
it matters little whether they are obliged to use a yard-stick or
a meter rod, pounds or kilograms, quarts or liters. The cost to
them is the cost of the few devices needed in weighing and
measuring ; the rationale of the system may never enter into
their thoughts." Thus, there is no reason why, so far as this
class of people is concerned, a change should not be made if the
new system supplied is superior for their purposes. This the
metric system is, on account of its great simplicity, doing away
as it does with all compound relations for the single ratio of ten,
connecting weight and measures by the weight of a volume of
water as a unit, thus eliminating all odd equivalents such as the
fact that a cubic foot of water weighs 62 \ pounds, and finally
doing away with such anomalies as dry and liquid measures of
capacity, avoirdupois, Troy, and apothecaries' weight, long tons
and short tons, hundredweight of 112 pounds, and other weights
and measures equally arbitrary, and not susceptible of being put
into simple relation with other quantities.
Indeed, the full complexity and absurdity of the present
" system," so called, is hardly realized until we stop to consider
that in the United States copper is weighed by one standard,
silver by another, medicines by a third, diamonds and other
precious stones by a fourth, and platinum and chemicals by a
fifth, none of which are interchangeable with one another except
by means of fractions. Nor is the condition less striking in the
case of the measures of capacity. One unit is used for wine, and
bears the same name as a dissimilar one used for grain, while
gas is measured by still a third unit. In fact, the condition as
regards the last-named groups of units is summed up in the
Anti-metric Argument of the committee of the American Society
of Mechanical Engineers, where it is stated in a passage already
quoted : l " There is no reason for the English system retaining
the gallon and the bushel, except that they are in such common
use." For convenience of computation it would be well if the
gallon were 216 cubic inches, or the cube of 6 inches, and the
1 See pp. 145, 146 ante; Transactions American Society of Mechanical Engineers,
vol. xxiv. 1902, No. 972, " Anti-Metric Argument," vii. p. 676.
THE METRIC SYSTEM FOR COMMERCE 163
bushel 1728 cubic inches, or 1 cubic foot. A few lines later in
this interesting argument some comments on the various units of
weight are concluded by the remark, " Both Troy weight and
apothecaries' weight might be abandoned." Here, from a source
unfriendly to the metric system, and opposed to any fundamental
changes in the weights and measures, is to be found a frank
admission that the measures of capacity are inconvenient, and
could be greatly improved, and that no reason other than use
exists for retaining the Troy and apothecaries' weight. Accord-
ingly, they propose to reconstruct the measures of capacity into a
new system which would occasion all the inconvenience attendant
on a transition from one system to another, and yet would not
yield the advantages of a decimal basis, and division, or relation
between weights and measures of the metric system, nor would it
have the least international value.
Likewise in England a society was formed in 1904 under the
title of the British Weights and Measures Association, which
had as it object " the defence, standardizing, and simplifying
(italics ours) of British weights and measures," and to oppose
the introduction of the meter as a British standard. Further-
more, this society proposed the introduction of "simplified and
scientifically related weights and measures based upon existing
British measures " (again italics ours). Now, with such an
admission that the Anglo-Saxon weights and measures need
" simplification " and to be " scientifically related," it is proposed
to proceed on a new basis, and construct and try a system
that has not been tested by actual use, as has the metric system,
and which in addition must be pushed against the latter, despite
the fact that it will doubtless contain neither the decimal basis
nor the relation between measures of length and weight. In
other words, there would be experienced all the inconvenience
which would attend a change to the metric system, and at the
same time the advantages obtained would be infinitely small in
comparison with what would follow a decision to adopt the
latter completely.
Moreover, such a proposition is by no means new, for we
have seen how Sir John Kiggs Miller, at the end of the
eighteenth century, advocated a decimal division of the British
weights and measures, while on October 27, 1863, Sir John
164 EVOLUTION OF WEIGHTS AND MEASURES
Herschel, the eminent scientist and astronomer, in an address
before the Leeds Astronomical Society, advocated the readjust-
ment of the British Imperial weights and measures on a decimal
basis according to a plan that at least appeared scientific and
methodical. He proposed to take as the standard of length the
earth's polar axis, which in imperial inches was computed to
be 500,482,296, and as a new, or as he termed it, " geometrical "
inch, employ the 5~o~o~tjoo 000 Part of tnis> wnicn would differ
by less than a thousandth from the customary inch, and be
at the same time related to a natural quantity. The unit
of weight would be a cubic foot of water, and would be
approximately equal to 1000 ounces avoirdupois. Herschel says :
" Thus the change, which would place our system of linear
measure on a perfectly faultless basis, would at the same time
rescue our weights and measures of capacity from their present
utter confusion, and secure that other advantage, second only
in importance to the former, of connecting them decimally with
that system on a regular, intelligible, and easily remembered
principle ; and that by an alteration practically inperceptible in
both cases, and interfering with no one of our usages or
denominations."
It might be said in passing that the length of the polar
radius, as calculated by Sir John Herschel, was no more
accurate or permanent than the original determination of the
length of the earth's quadrant by the founders of the metric
system, while similar, though greater, errors have been found
in his fundamental unit of weight. It is now conclusively
recognized in metrology that no terrestrial dimensions can be
relied upon to furnish an accurate standard of length.1 Thus
we see that a simple and albeit excellent step at reforming
British weights and measure did not meet with any greater
favor than the complete change to the metric system advocated
about the same time, and it is quite probable that a like fate
would to-day befall any similar proposition. So that the
question seems to be not to reform weights and measures by
gradual and slight improvements, but, if any changes can be
made, to adopt the best possible system, notwithstanding the
xSee Mendenhall, "The Metric System," Appleton's Popular Science Monthly,
October, 1896.
THE METRIC SYSTEM FOR COMMERCE 165
drawback of temporary inconvenience, and for the sake of the
future benefits which must unmistakably follow.
Perhaps the most important question in connection with
the adoption of the metric system is whether the change
would occasion any temporary inconvenience or expense to the
people at large. In the United States the great majority of
the people have been educated in the public schools, in most
of which since 1880 the metric system has been taught more or
less effectively as an integral part of arithmetic. Everyone
is used to the decimal system as employed in the national
currency and coinage, and, furthermore, it must be granted that
a higher standard of intelligence and adaptability prevails in
the United States than in Germany and other European
countries, where but little inconvenience was experienced and
practically no injury was done at the time of the change. True,
there would be in some cases the cost of new scales, weights,
and measures, but it must be remembered that these are under-
going constant deterioration, and in constant use the life of
scales and weights is only about two years. Therefore, any such
expense would be in actuality practically negligible, and doubtless
would result in distributing over the country weights and
measures of increased accuracy. Indisputably some time would
be required for the complete assimilation of metric measures and
weights, as we have seen was the case in Europe, but at the same
time the advantages attending their use would begin, and there
would be employed tables of legal equivalents which would soon
educate all to the necessary proficiency. Then, also, we would
see for a few years before and after any legislative establishment
of the metric system, all books for common use containing
formulas, recipes, etc., printed with all quantities in both English
and metric measures, so that the transition from one to the other
either ideally or actually would be attended with no inconvenience.
In addition to the marked advantages in the actual measuring
and weighing of everyday life, due to the simplicity of the
metric system, there would be the great saving of time in the
schools where the complete metric system taught in connection
with decimals would require but a fraction of the time now given
to compound numbers. In fact authorities on education have
estimated that at least one year of the child's school course could
166 EVOLUTION OF WEIGHTS AND MEASURES
be saved by the adoption of the metric system, as after its
employment in our practical everyday life, the Anglo-Saxon
measures would be of little more use than those of the Greeks
and Eomans, and would have scarcely more interest than the
old measures of France have to-day.
It is not necessary here to refer to the great saving of time in
making calculations involving quantities of produce of various
kind, although it is by no means unimportant, for with the class
of citizens we are now considering, while bookkeeping usually
plays but a secondary part in their life, yet it is employed, and
the farmer or petty shopkeeper will appreciate the saving of
time as much as the clerk or accountant whom we will consider
later. For the mechanic it is amply demonstrated that a change
in measurements makes but little difference as foreign workmen
educated to the metric system are able to work in the Anglo-
Saxon system without any difficulty whatsoever and vice versa,
ample testimony being forthcoming on both sides of this pro-
position.
In short, there are no serious drawbacks so far as the average
man and woman are concerned why America and Great Britain
should not adopt the metric system, and when it is recalled, how
practically no inconvenience was experienced in Canada when the
change was made from shillings and pence to dollars and cents,
or in the early days of the United States when its system of
currency was established on lines quite new, it is not reasonable
to anticipate any embarrassment or difficulty.
We are then brought face to face with the question, how will
the adoption of a metric system affect the internal commerce of a
country using the term as referring to the exchange of com-
modities on a somewhat larger scale than we have discussed
above. While such commerce depends for its prosperity on the
individual purchaser, yet anything which facilitates it acts to the
latter's benefit in reduction of prices and promptness of delivery
and improvement of quality. This exchange is accomplished
through an intricate system of machinery in which credits, banks,
transportation, and other factors all enter to a large degree. Yet,
with the extension of commerce constantly going on, there has
been no backward step, and in its progress simplicity and
accuracy in business transactions have been the chief essentials
THE METRIC SYSTEM FOR COMMERCE 167
which have been aimed at and attained. Thus the use of
banking facilities, and the telegraph, for the exchange of money
have contributed to save time and trouble, which in business are
definitely measured by money, while typewriter, telephone, cal-
culating machines, and new methods of bookkeeping have played
their part in releasing the mind of the business man to new and
original activities, and to the extension of his business along such
directions as his experience tells him are most profitable. With
such innovations must be considered the adoption of the metric
system, as a step in advance, since it will simplify all calculations
and bookkeeping by the elimination of useless multiplications
which are involved in the use of the compound numbers employed
in the ordinary weights and measures. One immediate result
would be the ease in determining errors and the decrease in their
number through less multiplication. Undeniably, the simplest
mathematical process for man is decimal multiplication, corre-
sponding as it does to his fundamental notation, and this simplicity
has been established uncontrovertibly in an experience of over a
century with the decimal system of American money, where there
has been demonstrated its applicability to all pecuniary trans-
actions, both large and small, from the actual handling of the
currency to the booking of credits and the computation of
discounts, interest, etc., not to mention the ease with which such
mental calculation as the determination of the price for a quantity
from a price for an individual article or vice versa can be made.
Consequently there has resulted the widespread use of per-
centages and a decimal division wherever possible. Thus, it is a
matter of convenience that railway and other shares shall be
valued on a percentage basis, and still more convenient that the
par value should be $100*00, and this practice has largely prevailed.
For mining or other shares where a smaller par value is desired,
it is usual to employ $10'00 or $1*00, while bonds are con-
veniently arranged on a basis of $1000*00 each. Likewise with
such commodities as sugar and cotton,1 where it is necessary
to express intermediate values between even cents, it has been
found desirable to give up common fraction and use a decimal
1 The Liverpool Cotton Association since October 1, 1902, has quoted cotton
values in hundredths of a penny instead of sixty-fourths. A similar practice is
observed in America.
168 EVOLUTION OF WEIGHTS AND MEASURES
division to facilitate computation and bookkeeping.1 These
changes have been the result of an evolution which has been
independent of any theory, but which has considered merely the
commercial availability of the method. For shop costs a decimal
hour is often employed, and such clocks are used in some
factories.
An instance of this in American weights and measures is
found in the tendency to eliminate as many units as possible, and
to use larger numerical figures, as 1000s of pounds instead of
tons. Another example was the introduction of the short ton of
2000 pounds to facilitate calculation, and this unit soon came to
be more extensively used than the long ton of 2240 pounds
inherited from Great Britain. No difficulty was experienced in
making the transition from the long to the short ton, in com-
mercial usage, and there is no reason why any inconvenience
should attend the change to the metric ton. In fact, in one of
the largest chemical works in the United States, — that of the
Solvay Process Company, — where the metric system is used
exclusively, it is customary to weigh the coal and other supplies,
when received, in metric units, despite the fact that they are
bought and invoiced in ordinary weights and measures. This
company has found it a distinct advantage in its internal
economy to make use of the metric system, and employs it in all
calculations, except for specifications of machinery and wood-work
that must be constructed outside of their factory by people to
whom the metric weights and measures are practically unknown.
An interesting example of the superiority of the metric system for
purposes of accounting and bookkeeping may be cited in the
experience of the Brighton Bailway in England, which for a
number of years has employed the kilogram as its unit of weight
for all its European business, and the French decimal monetary
system for its accounts.2 It is the opinion of the officials of this
road that the keeping of all accounts would be simplified by using
metric weights and measures. In the foreign business it would
1The Stock Exchanges, however, still use common fractions and commissions
are usually in eighths and sixteenths of a per cent.
2 See testimony of Charles A. de Pury, chief accountant of Brighton Railway in
Report by Select Committee on Weights and Measures (Metric System) Bill
[H.L.] 1904, p. 25.
THE METRIC SYSTEM FOR COMMERCE 169
have been possible, of course, to have changed the French weights
and currency to English, but the auditors of this corporation
believed that the metric system would be the more convenient,,
and such it has proved in practice.
The elimination of the middleman is one of the tendencies of
modern trade, and the more direct relation of consumer with
producer requires that business should be done on the simplest
possible basis by the contracting parties. Now the middleman
in the past was the one who usually made the transformations of
weights and measures, buying by one system and selling by
another. Inasmuch as often now he is considered superfluous,
in many transactions where the buyer and seller come together
directly, it is essential that a single system, which must also be
the simplest, should be employed. Thus there is no reason why
coal should be sold at wholesale by the long ton and retailed by
the short ton of 2000 pounds, or that the dealer in drugs and
chemicals imported by metric weights should dispose of them by
avoirdupois or apothecaries pounds. In fact, transformations of
weights and measures, or the use of double systems, are and
always have been a fruitful source of complaint and controversy.
Indeed, it was well said by a British diplomatic official in
speaking of conditions in Belgium, " The disputes which were
formerly so numerous, and which rendered long and complicated
calculations necessary, have become few and far between. In
short, the adoption of the metric system has done much to ensure
honesty in commercial transactions." !
With the decimal system can be used such important labor
saving device as slide-rules and calculating machines, the latter
in particular now being a feature of every well equipped office,
and resulting in increased accuracy and speed of operation. So
that the way is in part prepared for the introduction of the
metric system to denote units of quantity on account of its
decimal features, which would fit in completely with modern
business computation, and America could make the change with
greater facility than Great Britain, or even than that experienced
by any foreign country, on account of its simple currency system.
With the advent of the metric system would come the release
1 Reports from Her Majesty's Representatives in Europe on the Metric System>
part i. p. 8 ; English Parliamentary Accounts and Papers, 1900, vol. xc.
170 EVOLUTION OF WEIGHTS AND MEASURES
from the various heterogeneous arrangements of tables of length,
surface, volume, capacity, and mass in which binary, duodecimal,
and other relations are maintained and abandoned in accordance
with no consistent theory or system, constantly requiring refer-
ence to unwieldy tables and tedious calculation. Not only is
there saving in the time required to learn the metric system over
all others (and it is safe to say that any clerk working at a new
task where quantities or dimensions of a substance were involved
would have to brush up his knowledge of compound numbers
and tables, or proceed with extreme slowness and caution), but in
its application there is a most important gain of time. The
result is that more business can be transacted with a smaller
office force, and that the activity of clerks and computers can be
turned in other directions.
The disadvantages attending the introduction of the metric
system will be entirely of a temporary character, and if we may
take the experience of Germany as a guide, will prove far less
than is feared by the timid. The time lost by making trans-
formation from the old into the new weights and measures will
in reality prove much less than is anticipated, as such operations
doubtless will be performed with the aid of tables, such as will
be found in the appendix, which not only the government but
every industry doubtless will prepare to facilitate such work,
while for new calculations employing metric weights and measures
throughout there will be a great saving.
The difficulty of minds learning to think in a new system of
weights and measures is not so easily disposed of, but we have
seen how convenient and easily applied are some of the approxi-
mations, and we have only for most purposes to consider a yard
equal to ^ of a meter, two pounds equal to *9 kilogram, a liter a
quart, a long ton equivalent to a metric ton, etc. The relation
between volume and capacity should be appreciated greatly in
commercial work, as the capacity of a tank, reservoir, bin, or car
in appropriate units can readily be computed from its dimensions,
and then, knowing the specific gravity, by simple multiplication
the weight of its contents can be ascertained.
With all the inconveniences of the Anglo-Saxon systems of
weights and measures we are forced to consider a still more
serious difficulty, namely the growth of a dual system due to the
THE METRIC SYSTEM FOR COMMERCE 171
increased use of the metric system as permitted by statute. It
cannot be denied that the metric system has made great progress,
and that by the close connection of science with industry that it
is destined to be even more widely employed. Both systems
being legal, and the metric measures coming into more wide
spread use, there would result the perpetual necessity of con-
verting from one to the other in commercial transactions, and
while the nation was waiting for the ultimate survival of the
fittest system, or the birth of an ideal scheme, incalculable
inconvenience and damage would ensue, as has been shown many
times in the past where a nation at other times than at a
transition period has employed a double standard.
CHAPTEK VII.
THE METRIC SYSTEM IN MANUFACTURING AND
ENGINEERING.
The application of the metric system to manufacturing and
mechanical and other forms of constructive engineering, where
there has been long use of units of other systems, presents con-
fessedly the most serious aspect of the question of adopting the
international weights and measures. These branches of human
activity, it must be remembered, had their beginnings in most
humble and commonplace sources, such as the village smith, the
local carpenter, or even the aboriginal savage with his primitive
loom. In this respect they differ from electrical and civil
engineering, and applied chemistry, where the applications of
science and discovery have resulted in vast industries and
important technical professions. From their very inception these
latter have been dependent on the work of scientific men, using
the term broadly, and it has been possible to use such units and
measurements as they have recommended. That these units
can be developed rationally and systematically, as well as with
extreme simplicity we can see from the electrical units which
will be discussed in a subsequent chapter. But in mechanical
engineering and manufacturing simple processes and methods
have gradually been developed by the aid of scientific men,
and by applying their discoveries to every- day work, con-
sequently the engineers have been forced to use the units
and measures of the people rather than to develop and
rationalize such systems as would best commend themselves to
their judgment.
THE METRIC SYSTEM IN MANUFACTURING 173
Improved methods of manufacturing, however, have brought
about machinery and processes marked by simplicity and
efficiency, and while the advantages that will ensue ultimately
from the adoption of international weights and measures will
more than compensate for any temporary inconvenience, never-
theless, it must be admitted that the transition will involve some
serious problems and expense. Inasmuch as comparatively few
manufacturing processes, or at least individual plants, remain
stationary, but are constantly undergoing improvements either of
method or machinery, the possibility of adjustment to new
conditions, such as a new system of weights and measures, is not
so difficult as might at first be imagined. Oftentimes changes of
styles or classes of product are made that are far more funda-
mental than any changes that would be involved by new
measures, and natural wear and tear to machinery require
constant renewals and substitutions at intervals, and in many
shops it is considered good economy to strive for a maximum
output at the expense of individual machines and tools. Further-
more, conformation to standards, so necessary for successful
manufacturing, does not involve the blind adherence to such
standards, however honored and however universally observed,
after better standards have been evolved. That such a change in
units or standards can readily be made we know from numerous
instances in the past where various gauges, screw threads, screws,
etc., have been changed without undue confusion and expense. A
notable instance, inasmuch as the change was radical and funda-
mental, was made by the printers of the United States in 1883,
when the nomenclature of the different sizes of type was changed,
and a system of measuring by points adopted to take the place of
names in use for years. In fact, the adoption of various screw
threads in different countries, either in the interest of standard-
ization or to obtain a better screw, and even their modification,
has worked no great hardship, and such changes in car coupling
and other devices recommended from time to time in the United
States by the Master Car Builders' Association, involving as they
often do marked departures from sizes or styles in use by
different railroads, seem to be made speedily and effectively, and
without such expense as would occasion objection from controlling
officials.
174 EVOLUTION OF WEIGHTS AND MEASURES
Numerous instances where changes of systems and standards
dealing with actual concrete things may be cited to show how
readily changes in manufacturing and mechanical engineering
have been brought about, proving that it is not only under ideal
conditions, such as the change from local to standard time, or
in an improved calendar, that scientific reforms can be effected.
Once the people concerned are convinced of the need of the
change and the superiority of a new system, history shows that
the change can be made effectively and expeditiously, so that at
present it remains for the adherents of the metric system to
convince the manufacturing public by demonstrating its superiority
for their work, and to show how it may be adopted with the
smallest amount of inconvenience. Possibly this will best be
understood by considering briefly the relation of weights and
measures to manufacturing and constructive engineering. If a
single piece of machinery or a single fabric is to be produced,
it is of little moment what units of weight and measures are
employed by the designer, and what are used by the maker,
provided that both can understand each other, and provided that
time and expense are subordinate. That this is true is shown by
the ease with which American and English workmen can and do
work from continental designs prepared according to the metric
measures and vice versa on special orders. But when thousands
of the manufactured article are required, and time and economy
must be considered, or in other words, when the commercial
conditions of successful manufacturing have to be met, then the
influence of weights and measures as reflected in standards,
processes, and in numerous more or less direct ways, is felt.
We may start with the raw material, which may be in bulk as
in the case of ore, pig iron, crude chemicals, baled cotton or wool,
logs, etc., to cite but a few examples, or we may consider as raw
material, wire, sheet metal, structural shapes from the rolling mill,
yarn, boards, and other sawed or milled timber, to mention some of
the innumerable articles that enter into manufacturing processes.
In the case of the former class we have to consider the same
principles discussed in the last chapter, as the purchase of the
materials would be greatly simplified by having all invoices and
calculations of prices made in the metric system, consequently
there would be a saving of time to the office. The actual
THE METRIC SYSTEM IN MANUFACTURING 175
weighing would be the same under any system, though easier
with metric weights, but for the computations involved in mixing
or otherwise treating raw materials there would be a great saving
effected by using the metric system, as it would avoid the
employment of different classes of units, and would be throughout
on a strictly decimal basis. However in this no particularly
serious questions arise, but with the other class of raw materials
used in manufacturing, experience has shown and convenience
enforces the demand that they must be supplied of certain
dimensions which must be of sufficient variety to fill all reason-
able needs, prepared according to certain standards, and packed in
certain quantities. The dimensions or weights are taken, of
course, in conventional units, and the law of supply and demand,
modified by co-operative action and trade customs among manu-
facturers, consumers, and dealers, has resulted in the establishment
of certain standard sizes which not only are regularly carried in
stock, but for which have been calculated many tables dealing
with their weight, strength, elasticity, resistance, and other
characteristics useful to designer and maker alike. As a result
the majority of articles used in manufacturing and construction
are made only in standard sizes, for making which special
machinery has been prepared and adjusted, while articles of other
dimensions must be specially made at considerably greater
expense.
This policy of making articles in standard sizes has been
productive of the highest benefit to the manufacturer, and
the specialization that has been brought about in American
works and factories has contributed in no small degree to the
position in manufacturing that the United States now occupies
among the nations of the world. This system of standardiza-
tion is also advantageous to the consumer, who in turn
may be just as important a manufacturer, only turning out a
more finished or more complex article. Let us see how the
metric system would apply here. First, let us take the purely
arbitrary standards which have no even dimensions. For
example, flour is manufactured and usually sold 196 pounds net
to the barrel, yet there is no particular reason for this quantity,
since flour sold in sacks for export, where it may be stowed the
more readily in a vessel's hold, usually is packed 140 pounds to
176 EVOLUTION OF WEIGHTS AND MEASURES
a sack. Now, if there was any reason for preserving these
particular quantities they could be used in metric weights just as
readily as at present, but appreciate the convenience if barrels of
100 kilograms and sacks of exactly half that amount were
employed. True, the miller would have to adjust his automatic
scales for weighing his flour, but the product would be turned out
in even quantities, and the weight of carload or cargo would be told
at a glance from the number of barrels or sacks. Every trans-
action from the time that the flour left the mill until it was divided
by the retail grocer into 10 kilogram lots would be facilitated.
Then let us consider wire and sheet metals for which there
have been a number of gauges. These, for the most part, have
been and are, not only arbitrary but irregular and inconsistent, and
have stated the thickness in decimal fractions of inches, some of
which are expressed to the fifth or sixth place. If these numbers
are to be retained it is certainly just as easy to express the
thicknesses in fractions of a millimeter as^ of an inch, and in fact
this was officially done in the Act of March 3, 1893, when a
standard gauge for sheet and plate iron and steel was established
by Congress l in which the numbers were defined by equivalent
values in inches and millimeters. Consequently, under the
existing legal gauge, the adoption of the metric system would
cause no difference whatever in the making of sheet iron and
steel, and the customer would find the same legal sizes under the
metric system as before. While no wire gauge has been legalized,
yet, if any of the standard gauges is to be used, it is quite as
easy to consider the metric as the inch values since the decimal
fractions are no greater. The gauge system at best is bad in its
general aspect as it always requires an act of memory, and in
practice so inexact and unsatisfactory that certain large consumers
in the United States, notably the Great Electric Companies,
have instructed their draughting rooms and purchasing depart-
ments to always specify by actual dimensions in thousandths
of an inch expressed decimally. But so long as gauges are
generally used, it is necessary to consider just what they
signify and what part they play in mechanical operations.
Formed as they are of plates of sheet steel or other metal, with
holes or openings with which to test the various samples of
1C. 221, Sec. 1, 27 Stat., 746, K.S. 3570.
THE METRIC SYSTEM IN MANUFACTURING 177
materials, they are in practice often at the outset very inexact in
their graduations, and in any event they sooner or later become
so by the wear of constant use. As regards their graduation and
division the various standard gauges differ widely from one
another, and in individual cases, as has been said, they are hardly
■ever arranged systematically or methodically. This can readily
be appreciated by examining the tables in almost any standard
engineer's reference or so-called pocket book, but a hint can be
given by the following list, which shows the dimensions in
decimal parts of an inch for the same number (No. 2) of the
various gauges that are all in use in the United States.
Dimensions of No. 2 gauge according to different standards :
Inch.
American or Brown & Sharpe, - '25763
Birmingham or Stubs' Wire, - '284
Washburn & Moen M'fg Co., Worcester, Mass., - '2625
Imperial Wire Gauge, - - - - '276
Stubs' Steel Wire, " '219
U.S. Standard for Plate, ... - -265625
Twist Drill and Steel Wire Gauge, - - - '221
Screw Gauge for Machine and Wood Screws, - '08416
Thus it will be seen that material made according to any of the
•above gauges is not suitable to be used with that made by
another gauge, as for example there is no correspondence between
the gauge sizes of wire and th.€ twist drill which would make the
hole in which the wire might be inserted, or the size of the wire
and the wood or machine screw into which it might be made.
Consequently the present tendency is to abandon all arbitrary
gauges and work to decimal parts of an inch requiring all
materials to be furnished of such dimensions, a condition which
can be easily determined with great exactness by a micrometer
caliper of low cost. Now, the use of decimals presents no
inconvenience whatsoever to the average mechanic, so that at such
a transition period as regards standard sizes of materials, there is
every reason for adopting the metric system rather than waiting
until further standardization on an inch basis shall have occurred.
Instead of arbitrary gauge numbers millimeters and decimal
fractions could be employed, and there would be the advantage of
having a larger number of integral numbers and division by
M
178 EVOLUTION OF WEIGHTS AND MEASURES
tenths and hundredths, amply sufficing for all ordinary mechanical
work. The workmen, in their measurements, would employ the
same form of micrometer, the reading of which would be even
more simple, and much greater interchangeability would result
as soon as materials were furnished in a smaller number, but
standard sizes.
The tendency would be towards a more exact arrangement on
a metric basis. Such a movement would be gradual, and there
would be few occasions where any difficulty would be experienced.
Metric wire gauges were introduced in France in 1894, and have
proved satisfactory, their use increasing very rapidly. In fact, in
much work done with such materials, as sheet metal and wire, as
well as with other material, it is rarely necessary to look for the
strictest exactness in conforming to a certain gauge as the purpose
can be satisfied by an approximation, and the customary method
of payment being made on a basis of weight prevents any
imposition or injustice. As, however, new dies or rolls were
required, these would be carefully adjusted to metric gauge, and
the older sizes would gradually become obsolete, unless there
arose some special demand, while in the case of sheet metal it
would only be necessary to have a new setting of the rolls. It is
impossible to conceive of any injury being done the manufacturer,
for at the worst he has only to provide himself with a few new
adjuncts to his larger tools and a limited number of smaller tools,,
which are constantly being replaced.
Then take the case of the lumber mill, where planks, boards,
joists, etc., are turned out on an inch basis. How near do these
dimensions correspond in reality with the sizes they are sold for ?
In fact, in many instances planed boards of a certain dimension
do not gauge that dimension at all, but represent what remains-
after a board sawed approximately to that thickness has been
planed. The carpenter and the cabinetmaker do not demand so
high a degree of precision from the lumber dealer that the *4 of a
millimeter, between 25 millimeters and an inch (25*4 mm.) cannot
be disregarded, and here again it is found that most standard
sizes of lumber can be readily described in metric measures-
without the use of decimal fractions, and no new machinery
will be required except as new styles or sizes are demanded.
In actual manufacturing, after the adoption of the metric
THE METRIC SYSTEM IN MANUFACTURING 179
system, the first step would be the provision of facilities for
making various articles, such as sheet metal, paper, wire, cloth,
etc., according to metric dimensions. This would be to meet the
requirements of the government and other consumers, who
desired goods according to metric specifications. In other words,
the same process would be gone through with as occurs when a
large new or special order is received. As these orders would be
in metric sizes, and conformable approximately to those that
experience had taught were most serviceable for the particular
use for which they were designed, they would gradually become
standards, and would supplant the older sizes. In many cases
where materials are sold by weight, as paper and wire, the effect
of a change of dimensions would have no effect on the price,
while a minute change sufficient to adapt the material to a
regular metric dimension would in no way affect its usefulness to
the consumer, and should there be a slight increase in some
instances it would be balanced by a slight decrease in others.
Indeed, in many instances only the trimming or finishing would
be involved, and here it is probable that the waste material would
just as likely be less than the amount produced in making the
present sizes as it would be greater, and at any rate it could
doubtless be worked or utilized in some way, the difficulties can
hardly be called serious.
Linear measures and standards play a prominent part in all
mechanical operations, and here the superiority of the metric
system and its ready applicability may be shown. It has been
the practice to measure by successively halving the unit, and in
the case of the inch this has brought us down to such fractions as
^ and -^g, which are awkward both for computation and
observation on a scale. While it is quite natural to halve or
quarter a unit, yet to pursue this policy of binary subdivision too
far is extremely inconvenient. With the metric system in linear
as in other measurements it is possible to make use of any
decimal multiple or submultiple of the meter from the micron to
the myriameter as the base, according to the nature of the
measurement involved, and it is quite possible to use the half of
it simply by writing "5, or the quarter by writing *25, both
expressions requiring no more figures than the corresponding
common fractions, and involving no difficulty in case it is desired
180 EVOLUTION OF WEIGHTS AND MEASURES
to transpose to a higher or lower unit. Now, it has been found
better in actual experience when other fractions than a half or
quarter are desired, to divide decimally, and where accurate work
is demanded it has become the almost universal custom in the
United States among engineers and machinists to work in
hundredths and thousandths of inches, the practice being followed
from draughting room to shop. This practice involves the ex-
pression of all quantities in terms of a single unit, such as feet,
inches, or pounds, with the appropriate decimal fraction, and
demonstrates the availability of the decimal system for such
practical work, as well as for mere computation. This practice is
rapidly on the increase, due largely to the use of calipers and
gauges thus divided, so that the matter of decimal fractions
presents no disadvantage, but rather a convenience, to the
workman who has to make measurements.
As regards the linear units themselves ; if the workman
employs millimeters he has a unit which is a whole number, and
is superior to ^, as the latter is too large, and represents coarse
measurement and work. On the other hand ^ is too fine a
division for an ordinary scale, especially for a draughtsman, and
is only useful on a steel scale, with which few mechanics are
equipped, consequently the centimeter and millimeter are quite as
convenient as the inch, while the foot, which is rarely used in
modern mechanical engineering, is in no way missed. Even if we
consider the inch as the principal unit we are forced to use, either
its sixteenth part, or its tenth, hundredth, or thousandth, and in
reality we make such a fractional part our standard unit, and we
have the odd relation between such units and the greater ones,
the inch, and the foot, as compared with the simple decimal
relation of the metric linear measures. The yard and the meter
wherever desired are units of the same class, and what can be
done with one is equally possible with the other, not to mention,
of course, the advantage of the decimal relation of the meter to
its sub-multiples. But the great gain is that all calculations are
made in the same unit as the original measurement, and no
reductions, save the transfer of a decimal point, are ever
necessary. Contrast this with the English system where
measurements made in inches must be changed to feet or yards
for use with tables or vice versa.
THE METRIC SYSTEM IN MANUFACTURING 181
But in most manufacturing there is comparatively little or no
measuring for the workman to do, inasmuch as he is required
merely to make his work according to gauges, or templates,
or jigs, which are supplied to him by the tool room, where
they have been carefully worked out from the specifications
of the draughting room. Holes are bored and reamed to a
certain gauge, drills are set so that several will come down on
the piece of work at places previously determined by the jig, and
planers, shapers, milling machines, etc., are all operated in the
same way. But there must be some consideration of standards
and units in the draughting room and tool room, is the suggestion
immediately made, and here possibly would be one of the points
where difficulty might be encountered. It has been shown in
actual experience that the work of the draughtsman in preparing
plans according to metric measures is not only no harder, but is
facilitated considerably in actual drawing, and immeasurably so
if there are computations to be made. Now, in the construction
of gauges and tools the highest intelligence of the mechanical
force is employed, and here there are men not only having a
knowledge of current sizes and standards, but perfectly capable of
working in any kind of measures. In fact, the dimensions of
many gauges are merely nominal, and there is a greater or less
deviation from the stated dimensions, but which concern neither
draughtsman nor workman if all tools and gauges are harmonized
as they must be to these dimensions throughout the work. This,
of course, involves the use of micrometers and other adjuncts to
fine measuring, and this class of work can be done with greater
facility in the metric system, as is shown by its adoption by
makers of instruments of precision, opticians, and watchmakers
universally.1 If tools and gauges in the factory are to remain as
before the introduction of the metric measures, as they can be
1 The Swiss watchmakers were the first to employ a metric thread for small
screws, and the basis of the system was to start with a pitch or distance between
threads of one millimeter, and to decrease the pitch of each succeeding size by
ten per cent. In 1869 not only were metric threads adopted by the American
Watch Company for watches, but also throughout their factory, and all their
watchmaking machinery has been constructed on that basis. In Great Britain a
Committee of the British Association for the Advancement of Science appointed
to determine a gauge for small screws used in telegraph and electrical apparatus
reported in favor of the Swiss series of small screws, and the same was adopted.
182 EVOLUTION OF WEIGHTS AND MEASURES
without the slightest inconvenience, it is only necessary to
designate them by their metric values for purpose of computation,
and to continue employing them with their various shop numbers
as before. Where new standards and gauges are to be con-
structed, as they must be from time to time, then it would prove
desirable to use the metric measures, and the tendency will be to
work toward even dimensions and universal standards. Such a
tendency will be general, and if the manufacturer need tools,
which he must buy, he will soon find that the new ones carefully
standardized will be forthcoming in metric sizes, wherever any
changes are made from existing patterns and numbers. To such
a degree of exactness is this work now carried on in well-
organized American shops, that the highly skilled man in charge
of the tools will find little trouble in adopting the metric
dimensions.
Making the supposition now that a machine shop or factory is
required to work to actual correct dimensions in the metric
system, which, of course, is not contemplated by any movement
for the introduction of the new system, it does not mean that a
new equipment of tools must be procured. None of the larger
tools would be changed, as even in the case of the lathes a single
gear wheel connected to the lead screw enables metric threads to
be cut on an ordinary lathe with an inch lead screw and vice
versa, while the only important changes would be such small
tools as drills, reamers, taps, dies, etc., where in certain dimensions
a new size might be demanded, and these, if not already made
and in stock, as are gear cutters for cutting metric pitches x at
the present time in the United States and England, would soon
be provided by tool makers.
In this connection the cutting of screws may be discussed
more at length, as it is one of the principal undertakings in a
machine shop, and involves the greatest care in order to secure
high precision and interchangeability. Screw threads originally
are made upon a lathe where a cutting tool is given a lateral
motion by means of a screw known as a lead screw which
revolves in a nut attached to the tool carriage, and thus gives a
lateral motion to the tool. The object on which the screw is
being cut is also revolved, and the proper ratio of revolution
1 Bevel gears can be cut to metric pitch with the usual tools.
THE METRIC SYSTEM IN MANUFACTURING 183
between the two is maintained by suitable gearing. In the
United States and England lathes are usually designed to work
on an inch basis, and consequently the lead screw is so divided
and the corresponding gears furnished. But, by the use of one
change wheel with 127 teeth1 it is possible to arrange a lathe so
that with a lead screw divided on an inch basis metric threads
may be cut with an error that can only be detected by the most
refined methods, if at all, and such screws are entirely suitable
for all ordinary use, being correct to one part in 6350. By such
means are made the taps of hard steel with which holes are
threaded, and the dies that are used for the more rapid cutting
of threads on a large scale in the actual manufacture of screws
in quantities.
While the adoption of the metric system does not necessarily
involve the doing away with the present systems of screw threads
in the United States and England, which, however, are purely
arbitrary, and could be measured in millimeters with equal
facility, yet there is a metric thread which was approved at a
congress of engineering societies held at Zurich in October, 1898,
and again at an international conference held in October, 1900, at
Paris, delegates being present from all the important metric
nations of the Continent, including France, Germany, Switzerland,
and Italy. This form of thread was evolved by the Socidte*
d'Encouragement pour lTndustrie Rationale of France, having been
devised by M. Ed. Sauvage, and used for a number of years on
the French railways previous to its adoption by the society.
With slight modifications it was adopted as an international
standard for shape of thread and pitch, and is now known as the
Systeme International, abbreviated to S.I. or S.J. The shape of
this thread is practically the same as that of the U.S. standard
adopted by the U.S. Navy Department in 1868, and also known
as the Franklin Institute or Sellers Standard, from the name of
its inventor, William Sellers. The thread of the bolt or screw
consists in cross section of an equilateral triangle, giving an angle
of 60 degrees as compared with 55 degrees in the Whitworth
(British) standard, and the edges and bottom of the thread are
flattened by an amount equal to -^ the height. A modification
and improvement over the Sellers thread, as well as over the
1 This represents five times the ratio of the inch to the millimeter.
184 EVOLUTION OF WEIGHTS AND MEASURES
Whitworth thread, consists in allowing for clearance between the
base of a nut thread and the top of a bolt thread, though in
American machine shop practice it has been usual so to make
Common Sizes of Screw Threads.
Whitworth.
S.I.
(Inches.)
Diam.
(mm.)
Diam.
Diam.
Thds. per inch.
Increment.
Diam.
Pitch.
Increment.
i
20
i
6
1
2
f
16
i
8
1-25
2
i
12
1
10
1-5
2
1
11
i
12
1-75
4
J
10
i
16
2'
4
i
9
i
20
2*5
4.
i
8
i
24
3*
6
i*
7
1
4
30
3'5
6
H
7
i
36
4-
6
i*
6
i
42
4*5
6
. it
5
i
48
5
8
2
*J
i
56
5-5
8
n
4
i
2
64
6
8
n
4
i
72
6-5
8
2f
H
80
7'
3
H
the thread that there is such a clearance, the sides of the thread
and nut receiving the fit. In the S.I. thread this clearance amounts
to -^ of the thread in the form of a circular fillet tangent to the
thread's side, while the thread itself has a flat top. The pitches
THE METRIC SYSTEM IN MANUFACTURING 185
or distances between the threads increase regularly by a half
millimeter, with a "25 millimeter interval in some cases, as
between 1 and 2 millimeters. The rate of increase is much more
regular and simpler than in the case of the United States
standard thread, where in many places awkward fractions are
introduced. The pitch of the latter is finer, thus making a bolt
constructed on the Systeme International a trifle weaker, but the
difference is not serious, and no disastrous effects have been
experienced in actual use. The underlying symmetry and the
regularity are, however, features of great value, and the system at
the time of its adoption was thought worthy of widespread use,
even to supplant the Whitworth thread, which despite its English
basis has been in wide use for years even in metric countries.1
In watchmaking the metric thread is employed universally, the
Swiss system being taken as the standard ; while for small
machine screws used in electrical and other apparatus there is
the B.A. (British Association) standard, which is also metric
The latter thread was devised by a committee of distinguished
electricians and experimental physicists, and since its adoption
the regularity and symmetry of its divisions have been thoroughly
appreciated.
The change to the Sellers thread in the United States was
made without any paralysis of manufacturing industries or
serious injury to machine work, and the same was true when the
railroads adopted a standard screw thread and gauge on the
recommendation of a committee of the Master Car Builders'
Association, which reported in 1882. This report2 shows the
advantages to be gained by adopting and adhering to one system,
and outlines the problem that was solved by the late Professor
William A. Eogers and the Pratt and Whitney Company in
preparing suitable standards for adoption by all railroads. This
change was made in the course of a few years without undue
difficulty or expense, and since has been found amply justified,
illustrating most strikingly the advantages of a common standard
in a single industry.
1 Henry Hess, "The S.J. Standard Metric Thread in Continental Europe,"
American Machinist, p. 422, vol. xxiii. No. 18, May 3, 1900.
2M. N. Forney, Chairman, Railroad Gazette (New York), July 7, 1882, vol. xiv.
p. 407.
186 EVOLUTION OF WEIGHTS AND MEASURES
The adoption of the metric system, however, does not
necessarily involve the changing of the present excellent screw
system of the United States, as it is perfectly possible to get
along with arbitrary names and gauges based on original
standards, and well denned in terms of metric as well as the old
measures. Just as " tenpenny " nails are now spoken of, so
screws could be denned by number even if they were based on
obsolete linear measures and standards. On the other hand, if
the tendency should be towards a new international gauge it will
come gradually, and without undue inconvenience, as similar
changes have been made in the past.
In Great Britain, where possibly the standardizing of screws
and screw threads has not been developed so highly as in the
United States, the situation has been most excellently summed up
by Alexander Siemens, the well-known electrical engineer and
manufacturer. In his Presidential Address l before the (British)
Institution of Electrical Engineers, delivered November 10, 1904,
he said :
" As a last resort the expense of changing the screw threads
is urged against the change to the Metric System, and the
Continental practice of calling their system ' Whitworth thread '
is considered an incontrovertible proof that the metrical screw
thread is impracticable. If all taps and dies and leading screws
had to be exchanged at once, it would certainly be a costly affair,
but such a measure is not likely to be adopted, as no advantage
could result from it. For the real difficulty with screw threads
is that giving dimensions on paper is not sufficient to ensure that
the screws, manufactured according to such instructions in
•different works, are really interchangeable. This subject has
been investigated by a committee from the War Office, and their
conclusions throw a very interesting light on the controversy.
In their opinion it is only possible to obtain interchangeable
■screws, if the leading screws by which they are made have all
been cut on the same screw-cutting lathe, or are at least cut on
benches which are fitted with a leading screw manufactured on
the same original bench. If another link is interposed, differences
in the screws turned out become perceptible. As a consequence
of the finding of the committee a screw-cutting lathe has been set
1 Electrician (London), Nov. 11, 1904, p. 149.
THE METRIC SYSTEM IN MANUFACTURING 187
up at the National Physical Laboratory, where leading screws
for screw-cutting lathes are to be manufactured.1 The same
experience has been had in other countries, where nominally
* Whitworth's threads ' are used. It is not possible to make
screws interchangeable by prescribing their dimensions, the only
way is to obtain taps and dies or leading spindles cut by the
same tools. If it is a case of extreme accuracy, there is no
difficulty in cutting English thread by means of a metric lathe, or
vice versa."
To appreciate just what would be the immediate effects of
the adoption of the metric system in mechanical engineering it
is interesting to study the experience of a large engine works
and machine shop in England — Messrs. Willans and Robinson, of
Rugby — which enjoys a reputation for extremely accurate work
together with progressive ideas associated with the best engineer-
ing practice. This firm employs in its works the metric measures
of length, and not only are they preferred by their draughtsmen
and engineers, but also by the workmen in the shops, who did
not experience the slightest difficulty in accustoming themselves
to the new system or to employing it interchangeably with the
customary measures. Inasmuch as this shop has been and is
now experiencing some of the conditions attendant on a transition
period from the customary to the metric measures its experiences
are of interest. They employ bolts whose diameter is turned to
the nearest even millimeter larger than the size of thread and on
them cut a thread of the standard Whitworth pattern. One of
their engineers, Mr. Ernest R. Briggs, in describing the use of the
metric system in the shop's work has written:2 "I have seen new
machines built in the metric system side by side with existing
lines built in the English system, and I have seen standard
parts of one set of machines made to work in with standard
parts of the other set, and I have also made and sent into the
shops drawings in which a single large and complicated casting
has been figured in each system. I can make no defence for
1 The screw of this lathe is six feet in length, and is made of compressed steel,
the thread being cut with such accuracy that it is said to be correct to rjj^nr of
an inch at 60° Fahrenheit. The lathe is installed in a constant temperature
room at Bushy House. [Authors.]
2 Ernest R. Briggs, p. 450, vol. xxv. American Machinist, 1902; also a second
jaaper by the same author on p. 1347 of the same volume.
188 EVOLUTION OF WEIGHTS AND MEASURES
this latter, but it shows what can be done in working the two
systems side by side during the transition period."
In England there is at present the beginning of a lack of
uniformity, as during recent years much improved machinery has
been imported from the United States and from Germany and
Switzerland. The former has screws cut to the Sellers thread,
while in the latter the S.I. system is being widely and increas-
ingly used. Consequently, so long as English engineers will go
into the market for the best machinery irrespective of its source,
as is now the tendency of the best and most progressive manu-
facturers, there is bound to be an increasing lack of uniformity in
screws and screw-threads.
As to the effect of the introduction of the metric system into
the manufacture of machinery, we cannot do better than conclude
by quoting from the remarks of Mr. S. M. Vauclain, the superin-
tendent of the Baldwin Locomotive Works of Philadelphia, Pa.
Mr. Vauclain's testimony is not only interesting and most
valuable from his high reputation as a mechanical engineer, but
from the position that his company enjoys in the manufacturing
world. Locomotives from its works have been shipped all over
the world, while the actual manufacture has been systematized
and specialized to such an extent that unrivalled speed of con-
struction as well as largeness of output has been attained. Mr,
Yauclain says i1 "So far as the metric system is concerned from
a manufacturer's standpoint, it certainly should have no terrors.
Where — in what workshop — can you find a 'dozen men who will
measure the same piece of work and find the same result with
the ordinary 2-foot rule, or such scales as are ordinarily provided
for their use ? Could any manufacturer in America to-day rely
upon the accuracy of the measurement of its employees in its
products ? Instead of having first-class fits and interchange-
ability he would have first-class misfits and ruination of his
trade." Eeferring to the vast amount of fitting involved at the
Baldwin Works, where there is an output of five locomotives
daily and a force of workmen aggregating 11,500, Mr. Yauclain
goes on to say, " . . . it can readily be understood how poorly
these locomotives would be fitted together if we relied upon each
and every one of these 11,500 men to do the measuring necessary
1S. M. Vauclain, p. 414, vol. cliii. Journal of Franklin Institute, 1902.
THE METRIC SYSTEM IN MANUFACTURING 189
to fit these parts together with the drawings furnished by the
draughtsmen in their hands."
Discussing the actual relation of the measures to the work of
designing and construction, he says : " What is the natural
proceeding, then, in a workshop of this kind ; you receive the
drawings from the drawing room ; they are all made to, we will
say, the English measure — 12 inches to the foot, 3 feet to
the yard, or whatever you please — no matter how you may see fit
to speak of it ; but really and truly these drawings are not made
to the ordinary English measure: they are made to a scale which
is adopted, and which represents 12 inches to the foot, or 3 feet
to the yard, or so many sixteenths inches to an inch. The scale
that we have adopted in our draughting room is a scale of
2 inches to the foot, and in comparing everything that we look
at, we do not consider the foot at all : but if it is 2 inches long it
is a foot long."
"When a change of this kind would commence in any manu-
facturing establishment, it would first commence in the drawing-
room (because unless the drawings were made in accordance with
the metric system, the men in the shop could never work to it),
and there would be very few gauges in use in the shop that
would have to be changed, because the gauges do not depend
upon the figured dimensions on the drawings ; the drawings
would all be figured for the gauges. A certain gauge would be
called for instead of a certain dimension. In our works to-day
there is not a single hole drilled in a connecting rod where the
straps are fitted oh the stub ends of the rods, that is drilled to
a dimension ; the drawings do not refer to any dimensions ; we
have no use for dimensions, but we have for gauges. They are
marked to be drilled with a certain gauge and a certain bushing
piece. You could not use an inch and a quarter drill in a inch
and an eighth bushing. Whatever bushing you use determines
the size of the drill you are going to use ; and whatever gauge
you use determines the distance apart the holes may be and the
number of them, and the distance they are from the end to the
stub. The workman goes ahead and drills regardless of the
consequences in accordance with the gauge that is ordered on the
drawing ; and the result is that these parts are perfectly inter-
changeable, and hundreds and thousands of these parts are
190 EVOLUTION OF WEIGHTS AND MEASURES
duplicated from time to time and shipped to almost every country
on the face of the earth, and that without a single dimension
either metric or English on the card — simply the gauge number
calling for that part. This may be met with the remark that
those people who do not do their work with gauges would not
find it so easy to change ; but that is easily confronted by stating
that no first-class shop, or any shop, no matter how small it
might be, that desired to enter into competition with the world
would ever do its work in any other way and expect to succeed;
it would die a natural death sooner from the fact that it failed to
use gauges or jigs for the output of its work — even though it had
only one of a kind to make — much sooner than it would if it
undertook to use the metric system."1
1 S. M. Vauclain, p. 417, vol. cliii. Journal of the Franklin Institute.
CHAPTEE VIII.
METEIC SYSTEM IN MEDICINE AND PHAEMACY.
In no branches of scientific work is there greater need for
uniformity of weights and measures than in pharmacy and
medicine, where the entire world is drawn upon for drugs and
chemicals for therapeutic purposes, and where the latest dis-
coveries of such agents, or new methods of their use, are immedi-
ately communicated to the medical profession in every civilized
country. With uniformity of measures there would result uniformity
of treatment, and the ability to compare various methods in
different cases. In fact, there is no reason why the medical
profession should not be able to write and speak in the same
language as concerns their weights and measures throughout the
world just as much as the chemist and other workers in pure and
applied science; such a condition would also facilitate the exchange
of scientific information, which in the case of medical intelligence
would be of incalculable value. In addition to this must be
considered the commercial advantages to the general wholesale
drug trade, the manufacturing chemist, and the retail pharmacist,
due to the fact that many drugs are produced in metric-using
countries, and are there sold and exported according to such
measures. These same drugs, when they reach English-speaking
countries, customarily are sold according to avoirdupois weight,
and are then compounded according to apothecaries' weight — a
system which is a survival from mediaeval times, and which finds
few, if any, defenders on grounds other than its customary usage.
The fact, however, must be considered that the manufacture and
distribution of pharmaceutical products is a trade that is self-
192 EVOLUTION OF WEIGHTS AND MEASURES
contained, as it were, and we do not find the retail consumption
of drugs and chemicals save for medicinal purposes, where the
measurements are by spoonfuls or similar devices, and are usually
at the direction of a physician, a matter of great interest in the
daily life of the public. In other words, the buying, selling, and
compounding of drugs and chemicals concerns the physician and
pharmacist rather than the general public, who, however, are the
ultimate consumers, but whose wants are not such as to require
the use of any particular system of weights and measures, much
less to insist upon it. The use of the metric system among the
manufacturers and dealers in drugs and chemicals has been
constantly on the increase, in fact some of them furnish their
products altogether according to metric units. On the other
hand, the European chemical manufacturer must provide special
containers for all of his products intended for the American
market. Therefore, it is a fact that manufacturers and dealers in
drugs and chemicals are more than willing to adopt metric
weights and measures exclusively, if they are not already in use.
Furthermore, we know that the pharmacist is convinced of the
availability of the metric system inasmuch as it has been adopted
universally in continental Europe (in Germany since 1858), and
figures exclusively in the United States Pharmacopoeia, and con-
jointly in the British Pharmacopoeia of 1898. This brings us to
the medical profession, and here we find that in English-speaking
countries there has been great progress in the use of metric
weights and measures in writing prescriptions, but that owing to
the conservative tendencies of medical colleges it is by no means
general, and while the majority of pharmacists stand ready to
compound metric prescriptions, comparatively few American
practitioners write them. That there is no difficulty involved is
shown by the ease with which the system was adopted by the
United States Marine Hospital Service, the Medical Department
of the United States Army, and the Medical Department of the
United States Navy, as will be further explained below ; while the
fact that it is eminently desirable is demonstrated not only from
the testimony of those that have used it, but from resolutions
adopted at various times by representative national organizations
of physicians and surgeons. Despite the fact that there has been
no active campaign in behalf of the metric system waged among
METRIC SYSTEM IN MEDICINE 193
physicians there has been great progress, and when its advantages
-are more thoroughly realized it is believed there will be little
opposition to completely dropping the absurd antiquated apothe-
caries' weights. The science of medicine to-day is closely con-
nected with chemistry, physiology, biology, microscopy, and other
sciences in which measurement plays a most important part. For
example, in all experimental medicine the doses given to animals
are measured in metric measures, in pathology the dimensions of
an organ or any part of it are always stated in centimeters or
millimeters, while the oculist employs metric measures in all his
measures of focal length. In short, wherever medicine comes
into contact with natural or exact science we find that the metric
system is employed, and there is no reason why it should not be
used universally. The only excuse advanced is that the practi-
tioner has learned all his doses on the basis of the old measures,
and that any change not only might result in inconvenience but
in possible danger to the patient, inasmuch as a mistake that
might prove fatal could be made in writing out the quantities.
This is indeed a very weak objection, as the pharmacist or his
clerk is constantly on the lookout for errors of this or any other
kind in prescriptions. Furthermore, the more advanced physician
is constantly reading in medical journals of new methods of treat-
ment employed in Europe, where of course the metric weights
and measures are altogether employed, and desiring to adopt such
remedies in his own practice he must either employ the metric
measures, or translate them into English, either operation requir-
ing a knowledge of the metric system.
In pharmacy there are two different methods of compounding
prescriptions according to the metric system, which, while
fundamentally different, in their actual results do not occasion
any very serious discrepancies. In Continental Europe and in
countries where the metric system is exclusively used, it is the
practice to measure all substances entering into a prescription,
whether solid or liquid, by weight, and this consequently is
known as the gravimetric method. That is, the quantities are
denoted by grams, and in Germany no designation of the unit
follows the number, grams being understood in every case, as
no other units are employed for this purpose. This, of course,
furnishes a very accurate method; but in the United States and
N
194 EVOLUTION OF WEIGHTS AND MEASURES
Great Britain, where the metric system is used it is customary to
employ what is termed the volumetric method, where the fluids
are measured by volume or capacity measure, the quantities
being indicated in cubic centimeters. The solids, of course, are
weighed in grams, and it is usual to write after the number the
abbreviation gm. to distinguish from gr. denoting grains, as used
in the older system. Inasmuch as the specific gravity of water
is taken as unity, and one cubic centimeter of water at its
temperature of maximum density weighs one gram, it will be
seen that for water and other liquids of approximately the same
specific gravity there is no difference between the two methods,
and the majority of the liquids used in compounding prescrip-
tions are so near to water in specific gravity that little trouble
is occasioned; but there are a few instances in which this
difference is material, according as the liquid is either con-
siderably lighter or heavier than water. These few should be
borne in mind in comparing formulae on the gravimetric system
with those on the volumetric. Of the substances lighter than
water the most important are ether, whose specific gravity is '736
at 0°C. and spirits of nitrous ether, whose specific gravity is "837.
Consequently, speaking approximately, four parts by weight of
these liquids will occupy an equivalent space to five parts by
weight of water. Alcohol (proof spirit) sp. gr. 0*79 at 20°
Centigrade is another substance similar in this respect. On the
other hand, dealing with liquids heavier than water, we find
that glycerin stands in such a ratio that five parts by weight
of it occupy the same space as four parts of water, while with
syrup this ratio is four to three, and with chloroform three
to two. It is, of course, possible to indicate on the prescription
that the quantities are to be taken by weight; but except in
such cases as above noted, or in those of an extraordinary-
character, the volumetric method is employed, and not only
corresponds more closely with the older method, but also is
much more expeditious, as the fluids may be poured from
graduated measuring glasses in much less time than they could
be weighed.
The profession at large was not so quick to see the advantages
of the metric system as the medical departments of the United
States Government, and the first of these to adopt the innovation
METRIC SYSTEM IN MEDICINE 195
was the Marine Hospital Service, where, in accordance with
Department Circular 39, dated April 27th, 1878, it was ordered
that " The Medical Officers of the Marine Hospital Service will
hereafter, for all official, medical and pharmaceutical purposes,
make use of the Metric System of Weights and Measures."
This action, which was the first Government order issued in
the United States to make the use of the metric system obli-
gatory for any purpose whatever,1 followed the report made
to Surgeon-General John M. Woodworth, which was prepared
by Oscar Oldberg, Phar.D., then Chief Clerk and Acting Medical
Purveyor, U.S. Marine Hospital Service, in which he called
attention to the advantages of the metric system, and provided
the necessary rules for expressing quantities in that system,
and also described the necessary methods to be followed in
writing metric prescriptions.
In 1881 the Bureau of Medicine and Surgery in the U.S.
Navy adopted the system, as on April 15th of that year there
was approved by Secretary William H. Hunt a small volume
entitled, Instructions for Medical Officers of the United States Navy,
prepared by Medical Director Philip S. Wales, U.S.N". On
page 10, Article 2, Section 1, was the official direction that "the
Metric System of Weights and Measures shall hereafter be
employed in the Medical Department of the Navy." Accordingly,
the " Supply Table " in this volume was prepared on a metric
basis, and supplies have since been issued in accordance with
this system.
In 1894 the metric system was adopted by the medical
department of the United States Army, and was put into
operation under the provisions of the accompanying order.
WAR DEPARTMENT,
Surgeon General's Office,
Washington, April 13, 1894.
CIRCULAR :
Upon the publication of the new Supply Table and receipt of the new
forms, all requisitions, invoices, receipts, and returns pertaining to medical
supplies will be in accordance with the metric system of weights and
measures.
After the 30th day of June, 1894, the use of this system in writing
1 See Oldberg, Weights, Measures and Specific Gravity, Chicago, 1888, p. 18.
196 EVOLUTION OF WEIGHTS AND MEASURES
official prescriptions is desired ; on and after the 1st day of January, 1895,
such use is hereby ordered.
Metric measures, weights, and prescription blanks will soon be issued
to all posts without requisition.
Until medical supplies now in stock in troy and avoirdupois weights
are exhausted, the following approximate values may be considered as
equivalent in transferring original packages :
1 ounce = 30 grammes.
1 pound = \ kilogram.
1 fluid ounce = 30 cubic centimeters.
1 pint = 500 cubic centimeters.
1 quart = 1 liter.
1 yard = 1 meter.
GEO. M. STERNBERG,
Burgeon General, U.S. Army.
Approved :
Daniel S. Lamont,
Secretary of War.
This order was promptly carried out on the dates specified,
and all supplies were not only handled within the department,
but were purchased from dealers according to metric weights and
dimensions. In addition, the army surgeons began writing their
prescriptions on the metric basis without protest or difficulty,
and the system was soon in successful operation, and in 1902
was pronounced by Surgeon-General Sternberg as eminently
satisfactory, the General testifying before the Committee on
Coinage, Weights and Measures, Congress, February 15, 1902,
when asked why he would not go back to the old system :
" Because it (the metric system) is so decidedly superior. It is
working smoothly, and we have no difficulty whatever — no
protests on the part of the people we deal with, from whom
we purchase. The wholesale druggist must necessarily be
familiar with it." 1
General Sternberg also said that the principal reason for
the adoption of the system was the greater simplicity of the
decimal system, and furthermore it was successfully used in
other countries, and was a better system than the one in use.
An important test came in the Spanish-American War, when the
1 Page 83, The Metric System of Weights and Measures. Committee on Coinage,
Weights and Measures (Hearing), February 15, 1902.
METRIC SYSTEM IN MEDICINE 197
medical department was increased by a number of volunteer and
contract surgeons ; but the latter experienced no difficulty in
conforming to the regulations.
In England the feeling of the advanced members of the
medical profession has been most favourable to the metric *
system, and in 1904 the General Medical Council adopted
the following resolution in reference to the Bill then before
the House of Lords : " That the President (with the Chairman
of the Pharmacopoean Committee) be requested to inform the
Lord President of the Privy Council that in the opinion of
the Council it is desirable that, after a sufficient period to
be fixed by law, the metric system of weights and measures
should become the one legal system for the preparation and
dispensing of drugs and medicines ; that the Council would
view with favour the passing into law of a Bill such as that
now before Parliament, entitled the 'Weights and Measures
(Metric System) Bill ' ; and that in that event the Council
would be prepared to take all necessary steps to give effect
to the law by making the proper modifications in the British
Pharmacopoeia."
The correctness of the prescription when written in metric
units is much more likely to be ensured, as there is no possi-
bility of mistaking the various units, since but two are used
— the gram for solids, and the cubic centimeter for liquids.
In a prescription written in apothecaries' weights and measures,
on the other hand, not only are there numerous units — as
pounds, ounces, drachms, scruples, grains, minims, etc. — but
these are denoted by alchemistic characters which, at least in
the case of ounces and drachms, are susceptible of confusion.
Thus, not only is there the danger of errors in figures which
is common to both methods, but in the case of the older
system there are also the characters. Furthermore, with
apothecaries' weights it is customary to denote the quantities
by Roman figures or letters, which are much more readily
confused than the Arabic figures employed in metric prescrip-
tions. If the decimal line is used, as in a cash account, the
danger of a misplaced decimal point, or of an occasional dot
being taken as a point, is obviated. In fact, these possible
errors attributed to the metric system have been found by
198 EVOLUTION OF WEIGHTS AND MEASURES
experience to be altogether imaginary, for a misplaced decimal
point decreases or increases a dose ten-fold. The dispenser
would therefore detect the error at a glance. Then there is
the further advantage that it is possible to send by telegraph
• a metric prescription with far greater facility than one where
the Eoman characters are employed.
While the gravimetric method may be the most scientific
and exact, yet it must be remembered that the dose cannot
be administered to the patient in the great majority of cases
with anything like scientific accuracy, and it is usual to
employ various domestic glasses and spoons, which of course give
a volumetric measurement. In general certain rough equivalents
amply suffice, and the following measurements are used in the
United States and France:
A tea-spoonful = 1 fluid drachm, = 5 grams of water
A dessert-spoonful = 2 fluid drachms, = 10
A table-spoonful = J fluid ounce, = 15
A tumblerful = 8 fluid ounces, = 240
A wine glass (U.S.A.) = 2 „ „ =60
A wine glass (French) = 5 „ „ =150
CHAPTER IX.
INTERNATIONAL ELECTRICAL UNITS.
Beside the units incident to our every-day life which we
have already discussed, it is possible to derive from the
metric system in connection with the ordinary unit for the
measurement of time employed throughout the civilized world,
a complete system of units that will answer for the measure-
ment of any and all physical quantities. For such a system
it is necessary to have as the bases certain fundamental units,
and with them we may build up and extend the system as
occasion demands. It has been found that, starting with
units of length, mass, and time, a satisfactory system can be
evolved; and though there have been several such systems
proposed, yet the one founded on the centimeter as the unit
of length, the gram as the unit of mass, and the second as
the unit of time, has met with the greatest favour. It has
for many years been the only one employed in scientific
work, and has served as a basis for other and practical
units when such have been required or desired. As the
units mentioned have been adopted for most scientific work,
being as small as were convenient to employ in ordinary
measuring processes, it is easy to see why they were chosen
eventually as the basis of a system of units that should be
complete and symmetrical. From the names of the funda-
mental units this system is known as the C.G.S. system,
and it is our purpose to outline briefly its development in
order that we may trace the derivation of some of the ordi-
nary electrical units now in every-day use, and which are
200 EVOLUTION OF WEIGHTS AND MEASURES
essentially metric in their origin. The first suggestion of
such a system of units was due to Carl Friedrich Gauss, who
in 1832 proposed a system of so-called absolute units, which.
had as its base the fundamental units of length, mass, and
time. This system was devised by Gauss while engaged in
the study of terrestrial magnetism, in which the intensity of
the earth's magnetism, as well as the declination and dip,
was to be measured at different points in Europe. For this
purpose a German Magnetic Union had been organized by
Gauss and Alexander Von Humboldt, and was actively engaged
in magnetic studies from about 1834 to 1842. Previously there
had been no unit for the intensity of magnetism, and English
physicists had taken the intensity at London as the standard.
Gauss believed that it would be more scientific, as well as
more practical, if a system were devised which would be
independent of season or place, as well as of instruments and
external conditions. Accordingly, as the system which he
proposed in 1832 was based merely on the three fundamental
units mentioned, he termed it the Absolute System. In this-
system it was possible to derive all necessary units from the
three selected as fundamental ; thus a unit of velocity was
obtained by defining it as such a velocity as a body would
have in travelling unit distance in unit time. Unit accelera-
tion was the acceleration that a body would experience when
it gained or lost unit velocity in unit time. Then, for the
unit of force, it was only necessary to take such a force as
would impart unit velocity to unit mass in unit time — that
is, the unit acceleration. Consequently, when it came to
defining a unit of intensity of magnetism, Gauss took such a
quantity of magnetism as would exert unit force on a similar
quantity at unit distance.1 Now, as magnetic force was mani-
fested by the attraction or repulsion of a magnetic pole when
placed in a magnetic fluid, it would be possible to measure-
the force by mechanical methods, and for this he deduced
the necessary equations.
In this way, by mathematical processes which are interesting but.
i Resultate aus den Beobachtungen des Magnetischen Vereins, 1836-1842; Soc.
Gott. viii. 1832-1837; Pogg. Ann. xxviii. §§ 241, 591 (1833); Gauss, Werke,.
v. § 79-118.
INTERNATIONAL ELECTRICAL UNITS 201
need not be discussed here, it was possible for Gauss to determine
the intensity of the earth's magnetic field at any given point on
its surface. While the process of derivation was the same as for
the modern C.G.S. system, yet Gauss employed as the funda-
mental units in his Absolute System the millimeter as the unit
of length, the milligram as the unit of mass, and the second as the
unit of time. By similar reasoning, it was possible to define the
unit charge of electricity as such a charge as would act on a
similar charge at unit distance with unit force. So useful was
this idea of absolute measurement that it was straightway
adopted by Wilhelm Weber, (1804-1891) and found application in
his experiments to measure the intensity of an electric current,,
the intensity of electromotive force and of resistance ; the latter
investigation being further developed by Eudolf Kohlrausch
(1809-1858) in some most valuable investigations. Weber's work1
is remarkable not only for the fact that he applied absolute
measurements in electricity, but for his showing that electricity
was but a manifestation of mechanical energy, and consequently
could be measured in terms of length, mass, and time. There was,,
however, an important difference, in that it was not possible to
measure directly quantities of electricity, but it was necessary to
make such measurements by the effect on some external object.
For example, when Weber came to determine the intensity of an
electric current in absolute measurement, he found three ways
open to him. The first was to determine the strength of current
by its chemical or electrolytic effect. In other words, a unit
current would be that which decomposed a unit mass of water
into its chemical elements in unit time. Secondly, the magnetic
effect of the electric current also served as a basis for measuring
a current of electricity, and a unit of intensity of current he
defined as such a current as would exert, upon a magnet pole, the
same force as an infinitely small magnet of unit moment, placed
at the center of a closed circuit of unit area around which the
current should flow, and perpendicular to its plane. In other
words, he defined his unit of current according to the measure-
ments which could be made with a tangent galvanometer, as will
be described below. Then thirdly, the intensity of current could
1 Rosenberger, Geschichte der Physik, vol. iii. pp. 302, 514-519. Braunschweig,.
1890. Weber, Pogg. Ann. xcix, p. 11, 1855.
202 EVOLUTION OF WEIGHTS AND MEASURES
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204 EVOLUTION OF WEIGHTS AND MEASURES
also be measured by the effect of two currents flowing along
parallel conductors distant from each other by a unit length.
Following out these three methods, Weber made a series of
absolute measurements and found that they possessed a certain
ratio to each other. He also found that, with the galvanometer,
he was able to measure the quantity of electricity with which a
conductor was statically charged, by allowing it to be discharged
or flow to the earth through the galvanometer. Having thus
been able to measure the intensity of current in absolute units,
which (following the example of Gauss) were based on the
millimeter, milligram, and second, Weber then proceeded to make
absolute measurements of electromotive force. The absolute
unit of electromotive force he defined as that induced by unit
magnetic force in a circular conductor of unit area, if this
circular conductor were turned from a position parallel to the
direction of the magnetic force into one perpendicular to it in the
time of one second.1 Inasmuch as he was able to use the
magnetic field of the earth, whose intensity could be measured
accurately, and as by his previous experiments he was able to
measure the intensity of the current, using the apparatus known
as the earth inductor, he was soon able to make a direct
measurement of electromotive force. The earth inductor, it
may be said in passing, consisted of a large coil of wire whose
axis of revolution was perpendicular to the lines of magnetic
force, so that when the coil was revolved a current was induced
in it which could be measured by the galvanometer.
With methods for the absolute measurement of current and
electromotive force already known and defined, it only remained
to measure the resistance in absolute units, and this, of course,
followed from Ohm's law, which had been known since 1827.
According to this statement, the current was equal to the electro-
motive force divided by the resistance, and consequently it followed
that a unit of resistance would be that through which unit
electromotive force would produce unit current. This determina-
tion of the unit of resistance involved most elaborate experiments,
1 Rosenberger, vol. iii. p. 517; " Electrodynamische Massbestimmungen ins
besondere Widertandsmessen, " Abhandl. der K. 8. Gesellsch. I. § 197, 1852; Pogg.
Ann. lxxxii. § 337. Weber, Abhandl. bei Begriindung der K. S. Gesellschaft der
Wissenschaft, 1846 ; Abhandl. der K. 8. Gesellschaft d. Wissenschaft, I. 1852.
INTERNATIONAL ELECTRICAL UNITS 205
which are among the most celebrated in all experimental physics,
and their result was firmly to establish the absolute system on a
thoroughly scientific basis.
There were, previous to this, various arbitrary electrical units
suggested, and in more or less limited use.1 Thus various
lengths of copper, iron, or German silver wire of specified length,
weight, and cross-section were suggested and employed as units.
Perhaps the most conspicuous of these was the copper wire of
prescribed dimensions and weight which was recommended by
Jacobi,2 of St. Petersburg, in 1846, to the physicists of Europe as
the standard of normal resistance. This standard was determined
in absolute units of resistance by Weber, but it did not prove
entirely acceptable, owing to the changes taking place in the
copper with time, and owing to the difficulties experienced in
obtaining standard conditions. Accordingly, Werner Siemens, of
Berlin, proposed, in 1860, following the suggestion of Marie-
Davy made in 1843, to use mercury in defining the unit of resist-
ance, and as a standard, a column of this substance one meter in
length and one square millimeter in cross-section, measured at
0°C.3 This also was measured by Weber in 1861, and later
by Kohlrausch.
For electromotive force, it was customary at this time to
employ the electromotive force of a constant battery, such as the
Daniell cell, and in the case of a current, to make use of various
arbitrary units. With the increase in the scientific knowledge of
electricity, as well as in its industrial applications, such as the
telegraph and submarine cable, it was realized that, for practical
use, there should be a systematic and comprehensive system of
electrical units, which would be based on certain fixed standards,
and would be universally employed by electricians. This subject
was accordingly taken up in Great Britain by the British
Association for the Advancement of Science, and in 1861 a strong
committee, composed of leading physicists and electricians, was
appointed to investigate the subject and to report on suitable
units. The subject was discussed in all its many bearings by
1 For a list with bibliography, see Eosenberger, Geschichte der Physik, vol. iii.
pp. 519-520.
2 Jacobi, Comptes Rendus (Paris), p. 277, vol. xxxiii.
3W. Siemens, Poggendorff's Annalen, ex. p. 1, 1860.
206 EVOLUTION OF WEIGHTS AND MEASURES
this committee, Weber's and other experiments were repeated, and
the result was that an absolute system was adopted, only the
centimeter, gram, and second were employed as the fundamental
units in place of the millimeter, milligram, and second of Gauss
and Weber. This committee not only reported in favor of the
establishment of the C.G.S. system, but also fixed a certain
number of so-called practical units, which, with slight modifica-
tions, are now in universal use.
The reason for this was that a number of the C.G.S. absolute
units are either too large or too small to be employed in practical
work. For example, the electromotive force of an ordinary
Daniell cell would represent about 108 absolute units, and as the
electrician of that time dealt with electromotive forces of this
magnitude, rather than with those represented by a quantity so
much smaller, it was convenient to multiply the absolute unit by
108 to obtain a convenient practical unit, which was designated
by the name volt. Likewise with the ohm, or practical unit of
resistance, which represented 109 absolute units. But in the case
of the ampere, or unit of current, which, as we have seen, must
follow from Ohm's law, the difference was not so large, and the
absolute unit had merely to be divided by 10 to give the practical
unit. This Commission decided on the coulomb as the unit of
quantity, being 10 _1 absolute units, and being the quantity of
electricity conveyed by one ampere in one second. As a unit of
capacity, the farad, or 10 ~9 absolute units, was taken, and measured
the capacity of a condenser charged to a potential of one volt by
one coulomb. As a more useful unit still, the micro-farad, or 10 "&
part of a farad, was also established. For work, the joule was
taken, representing 107 ergs or absolute units of work, and
equivalent to the energy expended in one second by one ampere
flowing through a resistance of one ohm. As a unit of power,
the watt, or 107 ergs per second, represented the power of a
current of one ampere flowing under a pressure of one volt, or
one joule per second, and when multiplied by 1000 it gives the
kilowatt, which soon became common in electrical work in place
of the old familiar horse-power.1
i For an interesting historical presentation which includes the text of recent
legislation, see Wolff, " The So-called International Electrical Units," a paper
presented at the International Congresses of Electricians at St. Louis, 1904.
INTERNATIONAL ELECTRICAL UNITS 207
In 1865 this committee made a determination of the ohm, and
constructed a standard of platinum-silver to represent its value.
This standard, by law, represented the legal unit of resistance in
Great Britain, and was also known for many years as the B.A.
(British Association) unit ; in fact, holding its own, especially in
English-speaking countries, until the adoption of the international
ohm by the Chicago Congress of 1893.
Soon after this, the invention by Latimer Clark, in 1873, of a
constant cell, which was found to have, under certain conditions,
an electromotive force of 1*434 volts, furnished a standard of
electromotive force which, while not legally defined until some
years later, became widely used, and figured in many determina-
tions.
So thoroughly was the C.G.S. system thought out by the
British Association Committee, and so systematically were the
practical units determined and denned that, despite minor in-
accuracies, as shown by the experiments of German physicists, the
system was favorably considered at the International Congress of
Electricians held in Paris in 1881, and resolutions were adopted
in which the C.G.S. electro-magnetic units were chosen as the
fundamental units in terms of which the practical units should be
defined. At a meeting held in 1884 an international commis-
sion decided on the length of the column of mercury for the
standard ohm, and the legal ohm was denned as the resistance of
a column of mercury of one square millimeter section, and of 106
centimeters length at a temperature of melting ice.
The ampere was defined as a current corresponding to 10 -1
absolute C.G.S. electro-magnetic units, while the volt was defined
as an electromotive force which produced a current of one
ampere in a conductor whose resistance was a legal ohm. This
definition of the ohm did not carry with it universal acceptance,
and the legal ohm was not made legal in Great Britain or in the
United States ; but in the meantime a number of prominent
physicists, including Professor Henry A. Eowland in America and
Lord Eayleigh in England, carried on further investigations to
evaluate the true ohm, with the result that the length of the
mercury column was found to be nearly 106*3 centimeters, which
Reprinted in Bulletin No. 1, Bureau of Standards, Washington, D.C. See British
Association Reports on Electrical Standards (London, 1873).
208 EVOLUTION OF WEIGHTS AND MEASURES
accordingly was adopted by the British Association Committee in
1892, together with the definition of the column in length and
mass, rather than by length and cross-section.
Meanwhile, in 1889, another international congress of elec-
tricians was held at Paris, at which, in addition to a number of
decisions involving nomenclature, definitions of units of energy,
power, and inductance were adopted. The joule was selected as
the practical unit of energy and was defined as equal to 107 C.G.S.
units, being equivalent to the energy disengaged as heat in one
second by a current of one ampere flowing through a resistance
of one ohm. As a practical unit of power the watt was taken,
and was equal to 107 C.G.S. units, being the power of one joule
per second. For inductance the quadrant was chosen as the
practical unit, and was defined as equal to 10d centimeters. This
-congress also took the important step of recommending that the
power of various electric machines, such as dynamos, motors,
transformers, etc., should be rated in watts and kilowatts instead
of horse-power, and this practice has generally prevailed even in
non-metric countries such as Great Britain and America.
In 1893, in connection with the World's Columbian Exposition
at Chicago, an International Congress of Electricians was held,
and a Chamber of Delegates, composed of officials appointed by
the various Governments, proceeded to define and name the
various electrical units. By this time, owing to the increased use
of electric lighting, various forms of power transmission, electric
railways, and other important applications of electricity, the
subject was one of prime interest, and required the most careful
oonsideration of the Chamber of Delegates, which consisted of
many of the world's most eminent physicists and electrical
engineers. Its deliberations resulted in a series of recom-
mendations which were reported to the Congress, and referred to
the various nations of the world, by many of whom they were
subsequently embodied to a greater or less extent in legal
■enactments making the use of the new units obligatory. In the
United States such an Act was passed and approved, July 12, 1894.1
These resolutions contained the following recommendations :
" Resolved, — That the several Governments represented by the
delegates of this International Congress of Electricians be, and
1 Revised Statutes of the United States, Supplement, vol. ii. chap. 131, 1894.
INTERNATIONAL ELECTRICAL UNITS 209
they are hereby, recommended to formally adopt as legal units of
electrical measure the following: As a unit of resistance, the
international ohm, which is based upon the ohm, equal to 109
units of resistance of the Centimeter-Gramme-Second System of
electro- magnetic units, and is represented by the resistance offered
to an unvarying electric current by a column of mercury at the
temperature of melting ice 14*4521 grammes in mass, of a constant
cross-sectional area, and of the length of 106*3 centimeters.
" As a unit of current, the international ampere, which is one-
tenth of the unit of current of the C.G.S. system of electro-
magnetic units, and which is represented sufficiently well for
practical use by the unvarying current which, when passed
through a solution of nitrate of silver in water, and in accordance
with accompanying specifications deposits silver at the rate of
0*001118 of a gram per second.
" As a unit of electromotive force, the international volt, which
is the electromotive force that, steadily applied to a conductor
whose resistance is one international ohm, will produce a current
of one international ampere, and which is represented sufficiently
well for practical use by \^% of the electromotive force between
the poles or electrodes of the voltaic cell known as Clark's cell,
at a temperature of 15° C, and prepared in the manner described
in the accompanying specification.1
" As a unit of quantity, the international coulomb, which is the
quantity of electricity transferred by a current of one international
ampere in one second.
" As a unit of capacity, the international farad, which is the
capacity of a condenser charged to a potential of one international
volt by one international coulomb of electricity.
" As a unit of work, the joule, which is equal to 107 units of
work in the C.G.S. system, and which is represented sufficiently
well for practical use by the energy expended in one second by
an international ampere in an international ohm.
" As a unit of power, the watt, which is equal to 107 units of power
in the C.G.S. system, and which is represented sufficiently well for
practical use by work done at the rate of one joule per second.
1 No report was ever made by the committee to which the preparation of the
specifications was entrusted. Its members were Professors Helmholtz, Ayrton,
and Carhart, but the death of the first prevented the work.
O
210 EVOLUTION OF WEIGHTS AND MEASURES
" As a unit of induction, the henry, which is the induction in a
circuit when the electromotive force induced in this circuit is
one international volt, while the inducing current varies at the
rate of one ampere per second."
Specifications for Construction and Use of the Silver Voltameter.
• In the following specifications the term silver voltameter
means the arrangement of apparatus by means of which an
electric current is passed through a solution of nitrate of silver in
water. The silver voltameter measures the total electrical
quantity which has passed during the time of the experiment,
and by noting this time the time average of the current, or if the
current has been kept constant, the current itself, can be deduced.
In employing the silver voltameter to measure currents of
about one ampere the following arrangements should be adopted :
The kathode on which the silver is to be deposited should take
the form of a platinum bowl not less than 10 cms. in diameter
and from 4 to 5 cms. in depth.
The anode should be a plate of pure silver some 30 sq. cms. in
area and 2 or 3 mms. in thickness.
This is supported horizontally in the liquid near the top of the
solution by a platinum wire passed through holes in the plate at
opposite corners. To prevent the disintegrated silver which is
formed on the anode from falling on to the kathode, the anode
should be wrapped round with pure filter paper, secured at the
back with sealing wax.
The liquid should consist of a neutral solution of pure silver
nitrate, containing about 15 parts by weight of the nitrate to 85
parts of water.
The resistance of the voltameter changes somewhat as the
current passes. To prevent these changes having too great an
effect on the current, some resistance besides that of the volta-
meter should be inserted in the circuit. The total metallic
resistance of the circuit should not be less than 10 ohms.
In the United States the foregoing recommendations were
duly given force of law by an Act of Congress approved
July 12, 1894, one section of which provided that the National
INTERNATIONAL ELECTRICAL UNITS 211
Academy of Sciences should prepare detailed specifications for
the practical application of the definitions of the ampere and
volt. Such specifications were accordingly prepared by a com-
mittee x of the Academy, and were adopted by that body on
February 9, 1895. They are given in full below.
REPORT.
In the preparation of this report, in order to have the specifications accord
with international usage, free use has been made of the English Govern-
ment specifications and of certain papers prepared by Dr. K. Kahle of
Germany, and Prof. H. S. Carhart of this country.
SPECIFICATIONS FOR THE PRACTICAL APPLICATION OF THE
DEFINITIONS OF THE AMPERE AND VOLT.
Specification A. — The Ampere.
In employing the silver voltameter to measure currents of about 1 ampere,
the following arrangements shall be adopted :
The kathode on which the silver is to be deposited shall take the form of
a platinum bowl not less than 10 centimeters in diameter, and from 4 to 5
centimeters in depth.
The anode shall be a disk or plate of pure silver some 30 square centi-
meters in area and 2 or 3 millimeters in thickness.
This shall be supported horizontally in the liquid near the top of the
solution by a silver rod riveted through its center. To prevent the dis-
integrated silver which is formed on the anode from falling upon the
kathode, the anode shall be wrapped around with pure filter paper, secured
at the back by suitable folding.
The liquid shall consist of a neutral solution of pure silver nitrate, con-
taining about 15 parts by weight of the nitrate to 85 parts of water.
The resistance of the voltameter changes somewhat as the current passes.
To prevent these changes having too great an effect on the current, some
resistance besides that of the voltameter should be inserted in the circuit.
The total metallic resistance of the circuit should not be less than 10 ohms.
Method of making a measurement. — The platinum bowl is to be washed
consecutively with nitric acid, distilled water, and absolute alcohol ; it
is then to be dried at 160° C, and left to cool in a desiccator. When
thoroughly cool it is to be weighed carefully.
It is to be nearly filled with the solution and connected to the rest of the
circuit by being placed on a clean insulated copper support to which a
binding screw is attached.
1 Henry A. Rowland, Chairman ; Henry L. Abbot, George F. Barker, Charles
S. Hastings, Albert A. Michelson, John Trowbridge, Carl Barus.
212 EVOLUTION OF WEIGHTS AND MEASURES
The anode is then to be immersed in the solution so as to be well covered
by it and supported in that position ; the connections to the rest of the
circuit are then to be made.
Contact is to be made at the key, noting the time. The current is to
be allowed to pass for not less than half an hour, and the time of breaking
contact observed.
The solution is now to be removed from the bowl and the deposit washed
with distilled water and left to soak for at least six hours. It is then
to be rinsed successively with distilled water and absolute alcohol and
dried in a hot-air bath at a temperature of about 160° C. After cooling
in a desiccator it is to be weighed again. The gain in mass gives the silver
deposited.
To find the time average of the current in amperes, this mass, expressed
in grams, must be divided by the number of seconds during which the
current has passed and by 0*001 11 8.
In determining the constant of an instrument by this method, the current
should be kept as nearly uniform as possible, and the readings of the
instrument observed at frequent intervals of time. These observations
give a curve from which the reading corresponding to the mean current
(time-average of the current) can be found. The current, as calculated from
the voltameter results, corresponds to this reading.
The current used iu this experiment must be obtained from a battery,
and not from a dynamo, especially when the instrument to be calibrated is
an electrodynamometer.
Specification B.— The Volt.
Definition and properties of the cell. — The cell has for its positive electrode,
mercury, and for its negative electrode, amalgamated zinc ; the electrolyte
consists of a saturated solution of zinc sulphate and mercurous sulphate.
The electromotive force is 1*434 volts at 15° C, and between 10° C. and 25° C,
by the increase of 1° C. in temperature, the electromotive force decreases by
0*00115 of a volt.
1. Preparation of the mercury. — To secure purity, it should be first treated
with acid in the usual manner and subsequently distilled in vacuo.
2. Preparation of the zinc amalgam. — The zinc designated in commerce
as " commercially pure " can be used without further preparation. For the
preparation of the amalgam, 1 part by weight of zinc is to be added to
9 parts by weight of mercury, and both are to be heated in a porcelain dish
at 100° C, with moderate stirring until the zinc has been fully dissolved in
the mercury.
3. Preparation of the mercurous sulphate. — Take mercurous sulphate, pur-
chased as pure ; mix with it a small quantity of pure mercury, and wash the
whole thoroughly with cold distilled water by agitation in a bottle ; drain
off the water and repeat the process at least twice. After the last washing,
INTERNATIONAL ELECTRICAL UNITS 213
drain off as much of the water as possible. (For further details of
purification, see Note A.)
4. Preparation of the zinc sulphate solution. — Prepare a neutral saturated
solution of pure recrystallized zinc sulphate, free from iron, by mixing
distilled water with nearly twice its weight of crystals of pure zinc sulphate
and adding zinc oxide in the proportion of about 2 per cent, by weight of the
zinc sulphate crystals to neutralize any free acid. The crystals should
be dissolved with the aid of gentle heat, but the temperature to which
the solution is raised must not exceed 30° C. Mercurous sulphate, treated
as described in 3, shall be added in the proportion of about 12 per cent,
by weight of the zinc sulphate crystals to neutralize the free zinc oxide
remaining, and then the solution filtered, while still warm, into a stock
bottle. Crystals should form as it cools.
5. Preparation of the mercurous sulphate and zinc sulphate paste. — For
making the paste, 2 or 3 parts by weight of mercurous sulphate are to
be added to 1 by weight of mercury. If the sulphate be dry, it is to
be mixed with a paste consisting of zinc sulphate crystals and a con-
centrated zinc sulphate solution, so that the whole constitutes a stiff mass,
which is permeated throughout by zinc sulphate crystals and globules
of mercury. If the sulphate, however, be moist, only zinc sulphate crystals
are to be added ; care must, however, be taken that these occur in excess
and are not dissolved after continued standing. The mercury must, in
this case also, permeate the paste in little globules. It is advantageous
to crush the zinc sulphate crystals before using, since the paste can then be
better manipulated.
To set up the cell. — The containing glass vessel, . . . shall consist of
two limbs closed at the bottom and joined above to a common neck fitted
with a ground-glass stopper. The diameter of the limbs should be at
least 2 centimeters and their length at least 3 centimeters. The neck
should be not less than 1*5 centimeters in diameter. At the bottom of
each limb a platinum wire of about 0*4 millimeter diameter is sealed
through the glass.
To set up the cell, place in one limb pure mercury and in the other
hot liquid amalgam, containing 90 parts mercury and 10 parts zinc. The
platinum wires at the bottom must be completely covered by the mercury
and the amalgam respectively. On the mercury place a layer 1 centimeter
thick of the zinc and mercurous sulphate paste described in 5. Both this
paste and the zinc amalgam must then be covered with a layer of the
neutral zinc sulphate crystals 1 centimeter thick. The whole vessel must
then be filled with the saturated zinc sulphate solution, and the stopper
inserted so that it shall just touch it, leaving, however, a small bubble
to guard against breakage when the temperature rises.
Before finally inserting the glass stopper it is to be brushed around
its upper edge with a strong alcoholic solution of shellac and pressed firmly
in place. (For details of filling the cell, see Note B.)
214 EVOLUTION OF WEIGHTS AND MEASURES
NOTES TO THE SPECIFICATIONS.
(A) The mercurous sulphate. — The treatment of the mercurous sulphate
has for its object the removal of any mercuric sulphate which is often
present as an impurity.
Mercuric sulphate decomposes in the presence of water into an acid and
a basic sulphate. The latter is a yellow substance — turpeth mineral —
practically insoluble in water ; its presence, at any rate in moderate
quantities, has no effect on the cell. If, however, it be formed, the acid
sulphate is also formed. This is soluble in water, and the acid produced
affects the electromotive force. The object of the washings is to dissolve
and remove this acid sulphate, and for this purpose the three washings
described in the specification will suffice in nearly all cases. If, however,
much of the turpeth mineral be formed, it shows that there is a great
deal of the acid sulphate present, and it will then be wiser to obtain a
fresh sample of mercurous sulphate, rather than to try by repeated washings
to get rid of all the acid.
The free mercury helps in the process of removing the acid, for the
acid mercuric sulphate attacks it, forming mercurous sulphate.
Pure mercurous sulphate, when quite free from acid, shows on repeated
washing a faint yellow tinge, which is due to the formation of a basic
mercurous salt distinct from the turpeth mineral, or basic mercuric sulphate.
The appearance of this primrose-yellow tint may be taken as an indication
that all the acid has been removed ; the washing may with advantage
be continued until this tint appears.
(B) Filling the cell. — After thoroughly cleaning and drying the glass
vessel, place it in a hot-water bath. Then pass through the neck of the
vessel a thin glass tube reaching to the bottom, to serve for the introduction
of the amalgam. This tube should be as large as the glass vessel will
admit. It serves to protect the upper part of the cell from being soiled
with the amalgam. To fill in the amalgam, a clean dropping tube about
10 centimeters long, drawn out to a fine point, should be used. Its lower
end is brought under the surface of the amalgam, heated in a porcelain
dish, and some of the amalgam is drawn into the tube by means of the
rubber bulb. The point is then quickly cleaned of dross with filter paper,
and is passed through the wider tube to the bottom and emptied by pressing
the bulb. The point of the tube must be so fine that the amalgam will
come out only on squeezing the bulb. This process is repeated until the
limb contains the desired quantity of amalgam. The vessel is then
removed from the water bath. After cooling, the amalgam must adhere
to the glass, and must show a clean surface with a metallic luster.
For insertion of the mercury, a dropping tube with a long stem will
be found convenient. The paste may be poured in through a wide tube
reaching nearly down to the mercury and having a funnel-shaped top.
If the paste does not move down freely it may be pushed down with a
INTERNATIONAL ELECTRICAL UNITS 215
small glass rod. The paste and the amalgam are then both covered with
the zinc sulphate crystals before the concentrated zinc sulphate solution
is poured in. This should be added through a small funnel, so as to
leave the neck of the vessel clean and dry.
For convenience and security in handling, the cell may be mounted in
a suitable case, so as to be at all times open to inspection.
In using the cell, sudden variations of temperature should, as far as
possible, be avoided, since the changes in electromotive force lag behind
those of temperature.
Somewhat similar specifications were prepared by the Board of
Trade of Great Britain and were promulgated in an Order
in Council, August 23, 1894. The chief points of difference
besides phraseology were in the specifications for the Clark cell,
but these were in no way radical. Canada also adopted regula-
tions essentially in harmony with the above, as did France,
Austria, and Belgium ; while in Germany the measure of current
was made of prime importance, and the specifications for the
silver voltameter and the method of measurement are somewhat
modified.1
At the Paris International Electrical Congress of 1900 it was
decided to give the name of Gauss to the C.G.S. unit of magnetic
field intensity, or to such a field as would be produced by the
unit of magnetism at the distance of one centimeter, or, in other
words, such a field as would act on a unit pole with the force of
one dyne. Likewise the same congress gave sanction to the
name of Maxwell to denote the C.G.S. unit of magnetic flux or
the number of magnetic lines within a tube of force. The
magnetic flux would consequently be equal to the product of the
intensity of the field by the area, and the unit would be a single
magnetic line. Thus magnetic flux would correspond to current,
being dependent on the magnetomotive force and the magnetic
reluctance. This step was taken as these C.G.S. units were
employed in actual practice and apparatus was in common use
by means of which field intensities could be measured directly.
The name Jcilogauss is also employed to denote a thousand times
the unit. Other propositions have been made for names for the
C.G.S. magnetic units, but they have not yet been adopted legally
1 The full text of the various laws and regulations will be found in the
Appendix to Wolff's paper on the "So-called International Electrical Units,"
Bulletin of the Bureau of Standards (Washington, 1901), No. 1, vol. 1, pp. 61-76.
216 EVOLUTION OF WEIGHTS AND MEASURES
as they have not been considered essential, though strenuously
urged by many prominent electricians.
After the adoption of the resolution defining the electrical
units, at the Electrical Congress held at Chicago in 1893, and
their subsequent ratification, either in whole or in part, by various
governments, it was found that there were slight errors in these
definitions, especially in the electromotive force of the Clark
cell, which has been found to be nearer 1*433 volts than 1*434 as
defined. It was stated by some physicists that a cadmium
(Weston) cell1 was more constant, had a lower temperature
coefficient, and could be defined with greater accuracy, while
further researches on the Clark cell itself gave a value for its
electromotive force somewhat different from that stated in the
resolutions ; and, in fact, in Germany the value 1*4328 volts was
adopted as corresponding to the realized value of the ohm and
ampere. There was also a demand for new units, and for changes
in the nomenclature in the existing units. Consequently, at the
Electrical Congress held in connection with the St. Louis Exposi-
tion, 1904, a chamber of representatives of various governments
was in session to pass upon these propositions. It was the
opinion of the Chamber of Delegates that these propositions were
of sufficient character to warrant a thorough discussion, but, at
the same time, the delegates did not seem to be of the opinion
that they should be settled at such a meeting. Accordingly, they
resolved that a permanent Commission, consisting of representa-
tives from various governments, should be convened, and that to
such an International Commission should be entrusted the decision
of the matter. Such an international body would have much the
same duties as the International Commission of Weights and
Measures, and, without doubt, its deliberations and decisions
would be equally acceptable and important to electricians and
physicists.
In concluding this chapter on electrical units it is hardly
necessary to more than call attention to the great benefits that
1 The Weston cell has for its electrodes cadmium amalgam covered with a
layer of crystals of cadmium sulphate, and pure mercury in contact with a paste
of mercurous sulphate, cadmium sulphate crystals, and metallic mercury, while
the electrolyte is a saturated aqueous solution of zinc sulphate and mercurous
sulphate.
INTERNATIONAL ELECTRICAL UNITS 217
have been conferred on the electrical industry throughout the
world by the employment, in all countries, of one and the same
system of units of measurement. In fact, this condition has been
advanced as one of the reasons for the rapid growth of the
industry, and while various modifications of units have been
demanded and discussed, they have only been adopted after they
have been determined by an International Congress. No nation
or group of electricians or engineers has ever found fault with
the extensive use of the decimal system, and by the close con-
nection of electrical units with the metric system such workers
have been enabled to appreciate the advantages of the latter, so
that in non-metric countries the electrical professions unanimously
are found eagerly demanding its adoption. In fact, it has been
truly said by a British electrical engineer,1 than whom there is
no one more competent to discuss the subject in its many aspects,
that " so far as I am aware nobody has ever suggested that it
would be to the advantage of any country to start a system of
electrical units of its own."
1 Alexander Siemens, Presidential Address before the Institution of Electrical
Engineers of Great Britain, Nov. 10, 1904, Electrician (London), Nov. 11, 1904,
p. 149.
CHAPTEE X.
STANDARDS AND COMPARISON.
In all systems of weights and measures based on one or more
arbitrary fundamental units, the concrete representation of the
unit in the form of a standard is necessary, and the construction
and preservation of such a standard is a matter of primary
importance. The reference of all measures to an original standard
is essential for their correctness, and such a standard must be
maintained and preserved in its integrity for purposes of com-
parison by some responsible authority, which is thus able to
provide against the use of false weights and measures. Accord-
ingly, from earliest times, standards were constructed and pre-
served under the direction of kings and priests, and the temples
were a favorite place for their deposit. Later, this duty was
assumed by the government, and to-day in addition we find the
integrity of standards of weights and measures safeguarded by
international agreement.
The progress of the science of metrology is not only well
exemplified in these actual representations of various units, but
is intimately connected with the construction of the prototypes of
the fundamental standards. The mechanical processes and other
features involved in their construction have so improved with
time and with the growth of physical science, especially as it
involves a constantly increasing degree of exactness in measuring,
that the subject is one which warrants attention in even a brief
treatise on weights and measures. In fact, metrology has been
defined as : " That part of the science of measures which applies
itself specially to the determinations of prototypes representative
of the fundamental units of dimensions and of mass, of the
standards of the first order which are derived from the same, and
are employed in experimental researches, aiming at a high
STANDARDS AND COMPARISON 219
exactitude, as well as to the operations of diverse natures which
are the necessary corollaries." 1
That a standard should exactly represent a unit is of course
obvious, and what is usually the case, the definition of the unit is
derived from the standard, as is the definition of the British
imperial yard or the modern definition of the meter. Therefore
it is essential that the standard should be so constructed as to be
as nearly permanent and invariable as human ingenuity can con-
trive. As an example of the lack of permanence experienced in
standards, attention might be called to the fact that the secondary
standards of the British yard of 1855, which were distributed to
the various nations and laboratories, have since undergone careful
comparisons and remeasurements, and it is believed that in many
cases their lengths are not the same as when they were first
constructed.2
While it is physically impossible to secure absolute invari-
ability in standards, yet in their construction a material should be
chosen whose variations are well-determined functions of one or
more independent variables easy to measure. In practice, these
variations themselves ought to be very small, and the variables
upon which they depend susceptible of being determined with
high precision. The realization of these conditions represents
essentially what has been accomplished by the advance of metro-
logical science so far as exactness in standards is involved. In
the past, as we have seen, an extreme degree of precision in
measurement was not essential, nor could it be obtained with the
means at the disposal of the scientist or mechanician, but
improvements in this branch of science have been made to such an
extent that within two centuries the precision of standards of length
has been increased nearly a thousand fold. With the growth of
knowledge, it was realized that matter varied to a marked degree
under the influences of temperature, pressure, time, and other
conditions, so that in consequence, not only a unit must be defined
precisely, but the appropriate standard and its copies be so con-
1J. Rene Benoit, " De la Precision dans la Determination des Longuers en
Metrologie," p. 31, Rapports pre'sente's au Congres International de Physique, tome
1, Paris, 1900.
2 See Report, Superintendent U.S. Coast and Geodetic Survey, 1877. Appendix
12, pp. 180-181.
220 EVOLUTION OF WEIGHTS AND MEASURES
structed that they would be permanent, invariable and exact. In
designing and constructing a standard to fill these demands there
would be, consequently, a number of conditions to be satisfied.
First, there would be the natural wear of time, which would alter
easily the length of a measure or the mass of a weight, and could
only be guarded against by selecting a hard and durable material
which would resist abrasion. Then, there would be the question
of temperature effects, most important in all metrological work,
but hardly realized before the beginning of the 18th century. For
it will be remembered that, at different temperatures, a body
varies in length and volume, so that a standard of length, for
example, is only of unit length at one stated and defined tempera-
ture, being too long at a higher temperature and too short at a
lower temperature. Consequently, it is desirable that a standard
should be of a material affected as little as possible by heat, or,
in scientific language, having a low and regular coefficient of
expansion, and it is essential that this amount of expansion
should be known accurately, so that in case the standard is used
at other temperatures than that of the definition, the amount that
it is too large or too small may be taken into consideration and
allowed for, as by knowing accurately and applying the factor
which represents the variation in length, a measurement may be
made as exact as the original measurement on which the standard
is based. It is therefore necessary to exclude from consideration
materials having coefficients of expansion which vary con-
siderably at different temperatures, or which expand at a
different rate from that with which they contract.
The prime condition of a standard of length, and the same is
essentially true of standards of mass, is that it should consist of a
single bar, or piece of a single material, avoiding any joining of
several elements, such as by screws or by soldering. In fact, the
method used at the beginning of the 19th century, whereby a strip
of silver was inlaid on a brass bar, as in the Troughton scale, after
the fashion of the graduated circles of various modern instruments,
was soon found unsuitable for the standards of higher precision
which were demanded. The material selected should not only be
hard and highly elastic, but should have a surface that can be
polished readily, and engraved with the marks of terminal limits,
or of the divisions of the unit. For many years it was customary
STANDARDS AND COMPARISON 221
to construct the standards of iron or of brass — materials which
were easily oxidizable, and which were with difficulty obtained in
a pure and constant condition. For the standard of the meter,
known as the Meter of the Archives, platinum was used ; but later,
the material best suited for a standard was found to be an alloy
of platinum and iridium, and such was used for the international
prototype meter and kilogram and the national standards copied
therefrom. This material, however, being extremely expensive,
cannot be used generally where secondary standards for ordinary
exact measurements are desired, nor can rock crystal of which a
few standards of mass have been constructed.
A recent study of alloys, however, has resulted in finding
materials which possess many of the desired properties, such as
hardness and durability, and at the same time have a low
coefficient of expansion. One of the most recent of these, known
as invar, has resulted from experiments carried on at the
International Bureau of Weights and Measures, and has been
developed to a high degree of usefulness by M. Guillaume. This
metal, which consists of 36 parts of nickel to 64 of steel, has been
found available for measuring rods and wires for use in geodetic
operations, and seems destined to occupy a much wider field in
the future. Wires for measuring base lines made of this alloy
have been found to possess a coefficient of expansion in some
cases as low as '0000001 for a degree centigrade.1 In 1900 invar
standards and gauges were put on the market, and for all prac-
tical purposes permitted the disregarding of temperature effects.
In fact, it has been proposed to employ a heavy bar of this
material as the support of the observing microscopes in a com-
parator. Invar, however, is not quite steady and constant and
cannot be used for primary standards. In accurate surveying
such standards should be determined just before and after using
in the field.
From the early standards of length rectangular or cylindrical
in form, much improvement has been made and care is now
taken that the cross-section of the bar shall be of such design
1See Guillaume, " Les Procedes Rapides de la Geodesie Moderne," La Nature
(Paris), 1904, No. 1640, p. 339, and No. 1643, p. 395; id., Les Applications des
Aciers au Nickel, avec un Appendice sur la The'orie des Aciers au Nickel (Paris,
1904) ; id., La Convention du Metre (Paris, 1902), pp. 127 and 233.
222 EVOLUTION OF WEIGHTS AND MEASURES
that not only it shall possess maximum strength, but especially
that it will resist deformation by bending, which in accurate
measurements may cause considerable error. Thus in a linear
scale of considerable length as compared with its breadth and
thickness and, let us say, of rectangular section, where the
divisions are on the upper surface, it will be obvious that if it is
so supported that the ends hang lower than the centre, the upper
surface will form a convex curve, and the particles of the material
lying in such a surface will be stretched apart, and the distance A
to B will be greater than when the bar is straight as under
normal conditions.
If the ends of the scale were supported, rather than the centre,
the opposite conditions would prevail, and the marked distance
will be too short. This was recognised by Captain Kater, who
proposed the employment of a scale of small thickness which was
placed on a base whose surface was perfectly plane.1 A better
solution of the difficulty was to use the neutral fibres, as shown
by the dotted line CD, and for this purpose the British standard
of 1855 was constructed, as shown on pages 245 and 246, where the
unit distance is measured between lines on polished gold plugs, set
in two holes or wells, so that they lie in this so-called neutral plane.
This idea was more perfectly carried out in the standards of
the International Metric Commission, having the X-section as
shown on page 254, where the construction is such that the bar
possesses maximum rigidity with the minimum material and the
neutral plane in the line standard is easily accessible for measure-
ments throughout its length. In standards for small lengths, such
as the decimeter, such considerations as a desirable type of cross-
section and the placing of the divisions in a neutral plane,
naturally do not require careful consideration and can practically
1See Kater, "Investigation of the Curvature of Bars, produced by the In-
equalities of the supporting surface," Phil. Trans., 1830, p. 359. See also W. A.
Rogers, Proc. Amer. Acad. Arts and Sciences, vol. xv. 1879-80, p. 292.
STANDARDS AND COMPARISON 223
be neglected, but in meter or yard standards it is an important
consideration.
Then, as regards the actual means of denoting the distance, we
may have end standards (Stalon a touts) and line standards (4talon
a traits). The end standard represents the given unit by the
distance between the extreme boundary surfaces, as in the case of
any ordinary rule, or in the case of the inside measure, — the
distance between the interior surfaces of two extended arms, — the
object being to secure better protection for the surfaces employed
for measurement, and at the same time, to furnish a ready means
of comparing end measures with a standard, by simply bringing
them within the space included between the terminal arms.
With the other form of standard, the limits of the distance are
indicated by lines or sometimes dots. The line standard, of
course, can be used with a microscope with cross-hairs, or a
micrometer microscope, much more readily than an end standard,
as it is possible to effect an exact setting on even a coarse
line with much greater accuracy than on an edge, which
though imperceptibly worn to the naked eye, would appear
rough and indistinct when magnified by the microscope.
The line standard possesses a distinct advantage, where it is
divided throughout its whole length, as is usually the case, since
it is readily comparable with its own sub-divisions and with
smaller standards. On the other hand, the end standard con-
stitutes merely a standard for a single length, and does not lend
itself to direct comparisons with the ordinary standards of other
lengths in the laboratory or testing bureau, which in the case of
metric scales are usually divided into millimeters, with the centi-
meters and decimeters suitably marked. With a standard so
divided, standards of measure for other distances besides the
greatest one marked on its surface must be supplied.
In spite of the general tendency to use a line standard, rather
than an end standard, Bessel, in 1835, when he was preparing a
standard based on the seconds pendulum at Koenigsberg, used a
steel bar with sapphires set in its ends, to form a standard of length.
This standard of Koenigsberg was used as a basis for numerous
measurements of base lines in geodetic surveys in Europe.1
Though the line standard forms the most suitable, and in
1 P. 9, Guillaume, La Convention du Metre.
224 EVOLUTION OF WEIGHTS AND MEASURES
fact the only, standard for a modern prototype, and even for
secondary purposes, there are nevertheless occasions where stan-
dards of the end type can be conveniently used. Especially is
this the case in mechanical engineering, where various gauges
and shop standards must be constructed so as to be used readily
in the tool-room or machine shop for accurate measurements.
The methods of comparison are essentially similar to those
employed in comparing line standards. However, certain
variations of methods have been introduced, since it is
necessary to consider the terminal faces, which are susceptible
of wear and must be protected carefully. In addition to the
use of the microscope comparator, which is described below,
in connection with line standards, there are three methods
which can be used for this purpose, as follows :
First, the method of direct contact, which, while the simplest,
can also be made very accurate if properly used.
Second, by reflection of an object at the terminal surface.
Third, by interference fringes which are produced at the
ends of the scale to be measured.
In the method of contact, which is ordinarily employed
where a high degree of precision is unnecessary, it is usual
to employ such simple measuring devices as a screw micro-
meter, or a spherometer, or some less accurate form of instru-
ment, such as calipers or a beam compass. The second and
third methods are optical, and must be executed by a trained
physicist ; but they increase materially the range of precision,
and can afford results more accurate than are obtained in
comparing line standards.
The method of reflection was employed in comparing the
Meter of the Archives, an end standard, with the provisional
meter for the construction of the international prototype, and
also subsequently in the standardizing of certain end standards
of platinum-iridium, which were given to such nations as had
ordered them. This method consisted in observing the dis-
placement of the reflection of a line at the terminal surface
of the bar; and while under certain circumstances it was
exact, it required a study of the objectives of the microscope
and other features in order to insure its accuracy.
Employing this method, in 1881-82, a series of comparisons
STANDARDS AND COMPARISON 225
of the new standards was made at the Conservatoire des Arts
ot Metiers with the Meter of the Archives, taking into con-
sideration most carefully the question of temperature. It was
found that these comparisons, when reduced to 0 degrees C,
gave an accuracy of *6 of a micron for each standard.
In the method of interference use is made of the phenomenon
•of Newton's rings, whereby interference of light follows differ-
ences in the path of a beam, such as may be produced by
reflection from two different surfaces. It is necessary to have
■a fixed and determined surface as a plane of reference, and then
to consider the difference in the fringes that are produced
by light falling on two other surfaces at different times.
Considering now a line standard constructed, of approved
material and cross-section, it is naturally of primary import-
ance to provide the marks accurately limiting the distance.
These marks or traces are usually made with a diamond, and
are transverse to the axis of the bar. The method employed
is to place the bar, with the standard by which it is graduated,
•on the carriage of a special piece of apparatus, such as a com-
parator or dividing engine, which will be described below more
fully, with the cross-hairs of one of the microscopes accurately
•over the line of the standard scale. After a mark is made
on the scale to be graduated, both scales are moved until the
second mark of the standard scale is under the cross-hairs,
and another ruling is then made by the diamond. Or the
scales may remain stationary and the microscope and tracing
device be moved.
To divide a scale into millimeters or other divisions the
dividing engine is employed, an instrument in which the
•essential feature consists of an accurately constructed screw,
whose pitch (i.e. distance between threads), as well as its
oonstant and periodic errors, are known to a high degree of
precision. This screw, working in a suitable nut, moves a
table along a heavy metal supporting bench, and a metal or
glass bar on this table can be moved forward by regular and
successive intervals of length. Above the table is a tracing
device operating in a fixed vertical plane, and by this means
the desired divisions may be inscribed on the bar. Apparatus
of this kind has been constructed which is entirely automatic
p
226 EVOLUTION OF WEIGHTS AND MEASURES
in its movements, and which is able to mark the divisions
in millimeters on a scale a meter in length. Such machines
have means of correcting the errors in the screw, whether
they are constant or occur at different intervals of its length,
and also devices permitting corrections for temperature. Often
these machines are driven by an electric motor, and even the
differences in length of the marks denoting divisions of the
scale — as, for example, at every tenth millimeter — are made
longer automatically. A meter scale divided into millimeters
can be ruled with a machine of this description in the Inter-
national Bureau of Weights and Measures, in about sixteen hours,,
with an accuracy of two or three microns for each division.1
With the dividing engine or ruling machine of the late Pro-
fessor H. A. Eowland of the Johns Hopkins University, designed
for constructing diffraction gratings for spectroscopic work rather
than for making linear scales, as many as 20,000 lines to the inch,.
787*5 to the millimeter, could be ruled on speculum metal, and
gratings having as many as 120,000 lines have been made where-
the estimated error between any two lines was not thought to
exceed 2000000 °^ an mcn> or nearly the 80q0q of a millimeter.2
To secure the best results, the surface of the standard or scale
on which the lines are traced should be highly polished, and great
care should be taken, not only in the choice of the diamond or
tracing-tool, but in the actual operation. The line made should
be clear and sharp, not broader than is absolutely necessary, and
not appearing rough and indistinct when seen under the micro-
scope. In the national standard prototypes of the meter this line-
measures from 6 to 8 microns in width, but after it had been
ruled, it was thought that a much narrower line, say 2 or &
microns, could have been used with advantage, — securing, of
course, a sufficient depth to insure the permanent preservation of
the line. On both sides of the line at a distance of *5 mm.
are two parallel and similar lines, the distance between them
1M. Guillaume says, "It is essential in order to get very good lines to trace
very slowly, and in the studies made at the Bureau International it has been
found useful to trace the 1000 lines of the meter in millimeters in about 16 hours.
The inaccuracy in the position of either end line does not exceed two or three
microns, but of course the error of every interval of 1 mm. is much smaller."
2 See The Physical Papers of Henry A. Rowland (Baltimore, 1902), pp. 506-51 1„
691-697.
STANDARDS AND COMPARISON 227
forming a standard millimeter at each end of the scale, which
furnishes a check on the micrometer of the microscopes of the
comparator used to compare the scales. These transverse lines
are crossed by two longitudinal lines parallel to the axis of the
bar, and distant from each other *2 of a millimeter. Between
the intersections of these lines with the transverse lines is where
the standard distance is measured.
The important part played by temperature in exact determina-
tions and comparisons of standards of length, as well as of mass,
of course involves a means of measuring such temperatures. This
subject has received increasing attention in the course of time,
and it has been realized that exactitude in constructing standards
of length is only possible where the most accurate methods of
temperature measurements are employed, as the changes in length
or volume with temperature of course produces marked variations
from the standard unit. Since a linear unit is represented by the
length of a standard or bar of metal at a fixed and defined temper-
ature, at no other temperature will this bar have the standard
length, and consequently its exact length at such other tempera-
ture can only be ascertained by knowing the amount that it
expands for a unit (degree) of temperature, and the precise
temperature at which the measurement is made. Accordingly,
two thermometric measurements of great precision are involved,
one in determining the expansion of the material forming the
standard, or obtaining the coefficient of expansion of the bar,
and the other, in measuring the temperature at which the bar is
used. Now as the coefficient of expansion enters as a direct
factor in determining the exact length of a standard, it is
necessary to consider how far we can depend upon its accuracy,
and to realize that if this factor cannot be trusted beyond a
certain figure of decimals, then refinement of measuring with the
micrometer is quite superfluous.
In the first attempts at accurate measurement and comparison
of standards, as soon as temperature effects began to be considered,
mercury-in-glass thermometers were used, and in them for many
years a confidence was placed, which has been since found
entirely unwarranted. The gravity of this matter was realized
by physicists toward the middle of the 19th century, and at the
time of the construction of the international standards, it was
228 EVOLUTION OF WEIGHTS AND MEASURES
considered necessary to undertake a complete study of the
mercury-in -glass thermometer, and find within what limits its
accuracy could be trusted. So many sources of error were found
in the instruments as then constructed, due to the material used,
and to differences in its behaviour at different temperatures, as
well as to the difference in the coefficient of expansion of mercury
at different temperatures, that it was found necessary, after a
most thorough investigation, to adopt a gas thermometer in which
hydrogen was used as the expanding fluid. In this the expansion
of the gas indicates the temperature, and within certain limits it
is far more accurate than the mercurial thermometer. The latter,
however, when carefully studied and calibrated, can be referred to
the hydrogen scale with sufficient exactness for use at ordinary
temperatures. For purposes of standardizing, it has been found
necessary to refer all temperature measurements to the hydrogen
thermometer, and the study of exact thermometry made at the
International Bureau of Weights and Measures, has been one of
its most important scientific works. It has served to increase the
accuracy of the present standard of length and of mass, as well as
to raise materially the degree of precision in all measurements in
science in which temperature enters as a factor.1
Fundamental standards or prototypes are of course not avail-
able for general work, even where high precision is demanded,
but they must serve only as a basis for the construction and
testing of secondary standards which are divided throughout their
entire length. These are necessary for many purposes, and can
be used under conditions involving more or less wear.
The question of the permanence of these fundamental
standards, or more particularly that of the international prototype
meter is of primary importance. New methods involving greater
exactness in measurements and comparisons would avail little if
1 Good modern mercury thermometers made of hard glass alloy are of great
accuracy at moderately high temperatui'es, but their scale though very well
defined and reproducible is an arbitrary one and has no fixed relation with
theoretical phenomena, as is the case with the gas thermometer — Guillaume.
See Benoit, p. 75, Rapports Congres International de Physique, tome i. Paris,
1900. Guillaume, La Convention du Metre, Paris, 1902, p. 26, etc., for resume
of thermometric studies at the International Bureau of Weights and Measures ;
Traite de la Thermome'trie de Precision. Paris, 1889. Travaux et Me'moires,
Bureau International des Poids et Mesures, vol. i.-vi., x., xii., xiii.
STANDARDS AND COMPARISON 229
changes were taking place in the material of the standard bar
which would produce variations in its length. Evidence that
has accumulated in almost twenty years' experience with the
national standard meter bars does not indicate any substantial
changes that should give cause for anxiety in this respect, but at
the same time, the physicist is hardly in a position to guarantee
this permanence for a longer period of time, such as a century.
Recourse must be had, therefore, to a series of comparisons
of other standards among themselves and of providing new means
by which the integrity of the standard may be safeguarded.
The most satisfactory of these auxiliary means of protection is
the reference of the standard meter to a wave-length of light,
according to the method devised by Professor A. A. Michelson
and applied at the Bureau International des Poids et Mesures, to
which reference will be made in the course of a few pages. Thus
to-day the permanence of the meter is assured in that it is defined
in terms of a wave-length of cadmium light, with an exactitude
of one part in 1,000,000 or, in other words, of a micron.1
In comparing standards of length the earliest scientific device
employed was the use of some form of calipers or beam compass.
Thus in comparing an outside end standard with an inside end
standard, by placing the former between the projecting ends of
the latter, a measurement could readily be made. For com-
parisons of this kind, the inside end standards constructed of
metal were frequently embedded in a masonry wall at some
central and convenient point in a city. In comparing the toise
of Peru with that of the Grand Chatelet, we are told by the
Astronomer Lalande that the microscope, in connection with a
beam compass having very fine points, was used as early as
1735, and we also know that a similar device where the
jaws or points were moved by micrometer screws with divided
heads was employed in England by Graham, in 1742, in
making his comparison of standards of length.2 In the earliest
comparisons involved in the original determination of the meter
and the construction of the standard bars used for measuring
1 Benoit, p. 68, Rapports Congres International de Physique, vol. i. Paris, 1900.
2 See "Description of Standards and Use of Beam Compasses," Philosophical
Transactions, 1742-1743, vol. xlii. London.
230 EVOLUTION OF WEIGHTS AND MEASURES
the bases, the various scales to be measured and compared
were placed on a long plate of brass, having a fixed terminal
piece at one end, with which the ends of the scales were placed
in contact. Differences of length were determined by means of a
moving contact block and a small scale carefully divided. This
device, known as the rule of comparison, or the comparator of
Borda and also of Lenoir, which was believed for many years to
have been lost, was discovered by M. Wolf,1 and is now preserved
in the Observatory of Paris. It consists of a heavy strip of
copper, some 13 pieds (4*225 meters) long, 30 lignes (6*78 centi-
meters) in width, and 4 lignes (-9 centimeter) in thickness. The
movable piece is a smaller scale of copper, about 6 feet in length,
and divided into ten thousandths of a toise. It was movable
along the copper bar, and with it an exact reading of the length
of the scales to be compared could be made. There were verniers
ruled on the copper bar at different points, such as 12 pieds from
the extremity, for the comparison of geodetic base bars of 2 toises
length ; at 6 pieds for the comparison of toise standards ; at 3
pieds for the comparison of meters, etc. The verniers were
divided to read to tenths, so that it was possible to obtain the
Y^j part of the length of a toise.2
In this way a degree of precision equal to about ^tro °f a
ligne ('01 mm.) was obtained, which was practically ten times that
attained in the comparisons of the toise of Peru and that of the
Grand Chatelet half a century before. However, even greater
precision was demanded at this time, and accordingly, a lever
comparator was constructed by Lenoir, in which the long arm of
a lever magnified the distance traversed by a movable contact piece
in connection with a shorter arm, with the result that it was pos-
sible to read even smaller differences than those mentioned above.3
The next step marking progress and increased accuracy in the
comparison of standards was the use of the micrometer-microscope
which was devised by Troughton, of London, and was first em-
ployed by Sir George Shuckburgh, in 1796-8, in the measurement
of some line standards, which were then beginning to be employed
1 See Annates de VObservatoire de Paris; Me'moires, vol. 17, p. C 32.
2Bigourdan, p. 86, Le Systtme Me'trique, Paris, 1901.
3 Benoit, p. 34, Rapports pre'sentts au Gongres International de Physique, vol. i.
Paris, 1900.
STANDARDS AND COMPARISON 231
in metrology.1 This device has since played an important part
in all such comparisons, and the micrometer-microscope, in
improved form, figures in many instruments for this purpose. In
•Shuckburgh's comparator, the two microscopes were arranged
vertically on a metallic bar, and in one there were fixed cross-
hairs, and in the other, a movable system of cross-hairs connected
with the screw of a micrometer. The divisions of the head of
this screw corresponded to ten thousandths of an English inch.
The method of operating was to adjust one of the scales so that
the image of its line should appear at the cross-hairs of one of the
microscopes, the cross-hairs being set at the focus of the objective.
The other microscope would be so adjusted that its cross-hairs
would coincide with the image of the line at the opposite end of
the scale, or in case of a comparison with end standards, the cross-
hair would be set on the ends themselves. In making a com-
parison, a second scale was substituted for the first, and was
placed under the microscopes in the same position, one of the
lines, or the extremity of the scale (in case it were an end
standard) being made to take a position so that its image would
■correspond with the cross-hairs of the first microscope. If the
•other division were exactly equivalent to that of the first scale, it
would occupy the same position in the field of the second micro-
scope, but, in case there was a difference, this difference could be
measured by moving the movable cross-hairs with the micrometer
screw. The micrometer-microscope of Sir George Shuckburgh
was capable of reading to '0001 of an inch, or the -^ of a milli-
meter, and with this apparatus he made, in 1802, a comparison
between the British and French standards.
This idea for a comparator underwent subsequent improvements
about 1804 at the hands of Baily, also of England, who employed
in his apparatus, two microscopes, each provided with a micro-
meter and with an achromatic objective, by means of which
the image was made clearer and the magnification increased.
He also devised a method whereby the scales could be slid
under the microscopes, without touching them with the hands,
by arranging a carriage on a frame independent of the microscopes.
While this apparatus contained important improvements, never-
theless, in its construction, it lacked in solidity, and at the
1 Philosophical Transactions (London), 1798, p. 137.
232 EVOLUTION OF WEIGHTS AND MEASURES
same time was without adequate means of preserving the*
temperature of the rules constant. Accordingly, the commission
charged with the construction of the British Imperial Standards,,
in 1843, made important improvements in the comparator^
supplying the desired rigidity and strength by means of a
solid foundation for the microscopes, and providing for enclosing
the rules to be compared in a double-lined box, whose tempera-
ture was maintained constant at the desired temperature by
a circulation of water.
In France, also, the work of constructing and comparing
standards of length developed, and the progress towards exact-
ness made in that country during the nineteenth century, was
due in large part to the placing the service of weights and
measures in charge of the Conservatoire des Arts et Metiers-
There was constructed for this institution, by Gambey, a com-
parator with longitudinal displacement, which permitted the
comparison of both end and line standards, and at the same-
time allowed the defining lines to be marked upon them. The
result of improvements and the activity of this establishment,
was that much was accomplished in the semi-scientific and
industrial application of exact measurements, and the weights
and measures of France were brought to a higher degree of
precision.
In the United States, also, important comparisons were made
of the various scales presented by the French and British
Governments, with those in the Coast and Geodetic Survey..
But neither instruments nor methods represented any striking
departures from European practice, though the work itself was.
up to the high scientific standard maintained by this bureau
and was favorably commented on abroad. A useful and
accurate comparator, still in use, was constructed by Saxton
and was employed in making the early standards of length.1
While there have been no fundamental improvements in
the idea underlying the operation of comparing standards,,
within the last half-century, nevertheless by various mechanical
improvements and refinements, the range of accuracy has been
notably increased, so that to-day the modern comparator
represents an instrument susceptible of great precision in the
1 Executive Doc. 27, 34th Congress, 3rd Session.
STANDARDS AND COMPARISON 233
hands of a competent observer. The prime requisite of a com-
parator designed for such purposes as the comparison of a
prototype with national or other standards, is its stability, and
for that purpose the instrument is generally mounted on piers
of solid masonry, which are independent of the structural walls
of the building in which it is placed. It is essential that such a
building should be located in a place free from vibrations and
disturbances, such as would be produced by the traffic of a busy
street, or by machinery, or by a railway. The micrometer-
microscopes are mounted on heavy castings, set on separate piers
placed at approximate distances, if the comparator is to be used
for the comparison of standards of a single unit, as, for example,,
meter-bars. If, on the other hand, the comparator is of a
universal character, and must be used in the comparison of
various lengths, then the microscopes must be mounted on
solid carriages, which are capable of being moved along some
sort of a solid frame-work or firmly mounted beam. Equally
important with the microscopes is the arrangement for carrying
the scales which are to be compared. Some means must be-
provided to place them successively in the same position beneath
the microscopes, so that the difference in their length may be-
determined by means of the micrometers. These scales must be
maintained at the same temperature, and must be examined
under practically the same conditions. This involves, first, the
absolute uniformity of the temperature of the apparatus itself,
and for this purpose it should be installed in a room where
direct sunlight cannot penetrate and be surrounded by corridors,
enabling a constant temperature to be maintained. This requires,
naturally, an apartment of a considerable extent, provided with
thick walls, and specially designed doors and windows, as well
as various devices for maintaining automatically the desired
degree of temperature. The entire instrument may be surrounded
by a box through which penetrate only the eye-pieces of the
microscopes and the handles controlling the various parts of the
mechanism.
To keep the scales at the same temperature there is a movable
carriage which carries a double-walled box containing water.
In this box the scales are placed and the water is kept in
constant circulation by means of small agitators electrically
234 EVOLUTION OF WEIGHTS AND MEASURES
driven and in motion except at the moment of reading. A
number of thermometers arranged in close proximity to the scales
enable a series of accurate readings of the temperature to be made
with microscopes placed above for that purpose. It will readily
be seen that by changing the temperature of the surrounding
water, the amount of expansion of a scale can be measured.1
Improvements have been made in the micrometer-microscope
as well as in the rest of the apparatus, and particularly in the
screws which form the basis for moving the cross-hairs and
for measuring the amount of motion. These improvements
consist essentially of a frame carrying several sets of cross-wires
in pairs, which occupy a vertical position in the field of view
of the microscope. This frame is set at the focal plane of
the objective, and can be moved laterally by means of a screw
with a graduated head and handle. Such screws are so con-
structed that they are practically free from constant or periodic
error, and by means of a spring, any " back-lash " or lost motion
between the screw and nut is guarded against. The head of
the screw is graduated to a certain number of divisions, usually
100, so that a fractional part of the revolution of the screw
can be determined accurately. For example, if a pair of cross-
wires are focussed over a line of a scale, it is possible, by noting
the number of revolutions of the screw, to bring those cross-
wires over the next line, to determine the value of a single
revolution of the screw, and by means of its divided head and a
vernier, of minute fractions of a single revolution. Where cross-
wires of the ordinary or X type were once employed and a setting
made on the centre of the magnified division, it is now usual to
employ two vertical cross- wires, following a plan proposed by
Kupffer when preparing the Eussian standards, and to arrange
the setting with respect to the edges of the engraved line. This
lends itself to greater accuracy, as by means of the bright borders
of the image of the line a much sharper setting can be made
than where the magnified line was bisected by a single cross-
wire. The magnifying power of the microscope for accurate
comparisons ranges from 80 to 250 times, and in some few rare
cases even higher, the most serviceable power being determined
XA description of the Brunner Comparator of the International Bureau will be
found in Travaux et Mdmoires du Bureau International des Poids et Mesures, vol. 4.
STANDARDS AND COMPARISON 235
after considering the conditions, as, under many circumstances,
increased magnification introduces errors and does not result
in as satisfactory results as with the use of a lower power.1
There must also be considered the illumination of the face of
the rule, and it is now usual to provide direct illumination, rather
than oblique. This is accomplished by the use of a prism which
will reflect light from a distant source, such as an incandescent
lamp with a ground glass globe, to the scale and then to the
objective of the microscope. A transparent plate of plane glass
placed in the tube of the microscope at an angle of 45 degrees to
the axis, will also produce the same result, and is preferred by
some observers.
As regards the manner in which the adjustment of the scale is
•accomplished, two main divisions of comparators can be made, —
those which give the transverse movement of the scales, and those
in which the scales are moved longitudinally. A longitudinal
comparator is so arranged that the divisions of a standard can be
studied accurately ; for example, throughout the entire length ; or
standards of different lengths, whose differences exceed the
diameter of the field of the microscopes, can be measured with
facility. Thus from a standard meter, a bar or tape of several
times this length for use in measuring a base line or in surveying,
•can be standardized. In a comparator of this kind the scales
must be so adjusted that they lie with their axis either in a
perfectly straight line or exactly parallel.
In the comparators where the scales have a transverse move-
ment, as is the case with an instrument designed for comparing
two scales of the same length, the microscopes are mounted at a
fixed distance, and the scales are adjusted so that their axes are
parallel to a line connecting the two microscopes. The two
scales should rest in a carriage protected from changes of
temperature by means already described, and so arranged that
after being adjusted parallel to each other, they can be moved
under the two microscopes. Such an arrangement enables one to
study the relative expansion of scales of different materials, as the
measurement of the differences of length at a certain temperature
1 See W. A. Rogers, " On the Present State of the Question of Standards of
Length," Proceedings American Academy of Arts and Sciences, vol. xv. 1879-80,
pp. 290-291.
236 EVOLUTION OF WEIGHTS AND MEASURES
can be made, and then, at a second temperature, obtained by
varying the warmth of the circulating water.
With standards of mass, the material of which they are com-
posed is of primary importance. Not only must the standard be
of a permanent character, hard and able to resist abrasion in actual
use, but it must be such that it will not be affected by the oxygen
of the air, or, in other words, have its surface oxidized and the
weight increased. Other and more subtle chemical changes must
also be provided against. On this account, platinum and rock
crystal have been found to be the most useful materials, and the
former posesses the merit of having a high specific gravity, so
that when weighed in air the amount displaced is a minimum.
Furthermore, the shape must be such that the volume can be
measured with a high degree of exactitude, as on the volume
depends the effect of buoyancy, and of temperature. Such cor-
rections are often very small ; in fact, much less than in the
case of a standard of length, but in constructing and using a
standard of mass, the barometric pressure, temperature, and the
humidity should be determined, as the density of the air must
be known accurately and duly considered.
In addition to possessing a geometrical figure easily measured,
the standard should be so designed that there are no grooves or
cavities to collect dust, and that when used in a balance it will
conform to the needs of the mechanism used for changing the
weights in the scale-pans. Taking all things into considera-
tion, the cylindrical shape with round edges serves the best,
and such is the form of the Kilogram of the Archives and of
the International Prototype and its copies.
For determining standards of mass, the modern physicist
has recourse to the same instrument which was employed thou-
sands of years ago by the ancients, viz. the balance with equal
arms. But he has effected such improvements in its mechanical
construction and operation that this instrument is now entitled to
rank with the apparatus of precision of the first order. For
accurate weighing, the balance must be of the finest and most
accurate workmanship, and also there must be employed various
methods and corrections evolved largely from mathematical
considerations.
In comparing standards of mass, and in all accurate weighings-
STANDARDS AND COMPARISON 237
with a balance, it is necessary to take into consideration the
buoyant effect of the displaced air, as conditions are quite
•different from those obtained when a body is weighed in a
vacuum. This correction is especially necessary in making an
■absolute determination, but in cases where the standard and
the weights with which it is compared are of the same material,
the effect is the same in both cases and does not enter into
consideration at all.
For accurate weighing it is possible to employ the method
of double weighing of Borda, where the two objects whose masses
are to be compared are successively placed in the same scale-
pan and are counterpoised by weights on the opposite side, or
the interchange of the weights on the scale-pans, as devised by
Gauss. There must be considered, also, the effect of temperature,
which can change the condition of balances and weights, just as
much as in other physical operations, and it is accordingly
necessary to have such a balance placed in a room with constant
temperature, and to provide against currents of air, by means of a
suitable case. Even the influence of the temperature of the
•observer's body has its effect, and he must be placed as far as
possible from the balance, observing the oscillation of the beam
with a small telescope, and changing the weights, setting the
beam in motion and bringing it to rest, and performing other
necessary operations by suitable mechanical devices, which can
be operated at a distance, without opening the casing of the
balance.
These conditions are realized in the balances used at the
Bureau International, as well as at various governmental
Bureaus of Standards, physical laboratories and like institutions.
Typical, perhaps, as involving the greatest refinements, are the
balances of the Bureau International, two forms of which are
•described in outline below.
Of these perhaps the simplest is the Ruprecht type of balance,
which consists of a balance with equal arms carrying two scale-
pans in which an opening is cut in the form of a cross, the edge
being cut away at one of the branches. Beneath this is an axis
carrying a cross-shaped piece of somewhat smaller dimensions
than the opening in the scale-pan. Two supports similar in
shape to the scale-pans and provided with like openings are
238 EVOLUTION OF WEIGHTS AND MEASURES
attached to the central column supporting the balance. When
a weight is placed on the scale-pan by means of mechanism
operated from a distance of over four meters, it is possible for the
cross-shaped piece below to be raised, thus carrying the weight
clear of the scale-pan, and then to be swung out through the
opening clear of the latter, and into the plate placed on the
central column where the weight may be deposited. The
standard carrying the cross-shaped piece is then lowered
and the weight is left on the rest. The weights can then be
revolved around the central column carrying the beam and by the
apparatus just mentioned placed on opposite pans from their
original position. This operation is accomplished by means of
gears and shafts, and is carried on simultaneously for both pans
of the balance. Mechanism is also provided, so that the observer
may release the pans and also the beam, by turning suitable
cranks, and there is a telescope, whereby he may observe the
deflections of the beam by means of a mirror and divided scale.1
The Bunge balance, at the Bureau International des Poids et
Mesures, contains several features leading to further refinements.
It is enclosed in a copper case, from which the air may be
exhausted, so that the weights may be compared in vacuo. In
addition to the means of changing the weights, and for releasing
and arresting the scale-pans and beam, mechanism is provided
whereby small additional weights can be added to one side or the
other of the beam, as is found necessary. All of the controlling
devices are so arranged that they may be operated by the
observer from a distance of several meters, and with this balance
the most accurate results may be obtained.
In the determination of standards of mass, it is necessary to
determine their specific gravity and the amount of water that
they displace when immersed. For this hydrostatic balances
are used, which, in their essential features, correspond with the
balances of precision just described. The vessel containing the
water in which the weight is immersed is placed directly below
1 Guillaume's La Convention du Metre, p. 111. The balances have been pro-
vided with suitable mechanism to add small differential weights, i.e. at the same
time two weights say of 100 and 100*5 milligrams respectively, which give a new
position of equilibrium and allow the determination of the sensitiveness. This-
addition of small weights can be made without arresting the balance which con-
stitutes a great saving of time. — Ch. Ed. Guillaume.
STANDARDS AND COMPARISON 239
the point of support of one of the arms of the balance. There
is also provided a scale-pan, in which the body to be measured
is placed, and connected with it — a device by which it can be
supported when immersed in water — the whole forming a con-
tinuous arrangement supported from one arm. The body is first
placed in the upper pan and counterbalanced by weights on the
opposite side of the balance. It is then removed and weights
are added in its place until the equilibrium of the balance is
secured. The sum of the weights so added gives, of course, the
actual weight of the body. It is then immersed in water, and
the same process is gone through with, the temperature of the
water being noted by a carefully calibrated thermometer. Various
devices are employed to secure a uniform temperature of the
water, to diminish the effects of friction and capillarity, and to
facilitate the handling of the body when immersed.
The sensibility of an accurate balance depends on the load,
and in making a weighing, this factor must be determined
accurately, and it is likely to vary under different conditions.
With the balances employed in comparing the standard kilo-
grams, it is usual to have the sensibility equal to 25 to 50
divisions for a milligram, or, in other words, an addition of
weight equal to a milligram produces a deflection of the beam
corresponding to this amount. This is useful, inasmuch as the
differences of weight between the two standards compared are
usually so small as to be measured only by the deflection, and not
requiring the addition of the smaller weights to either scale-pan.
In some cases, a reading of a tenth of a division of the
deflection in either direction may correspond to some thousandths
of a milligram. Thus, in comparisons of standard kilograms, the
•01 of a milligram would be equal to a '000,000,01 of the mass
measured, but other considerations do not permit this degree of
precision to be maintained. Nevertheless, this represents a
substantial gain in accuracy, as the fine balance used at the
London Mint by Harris in 1743 was able to indicate only ^ of
a grain on a Troy pound, or about one part in 50,000, while in
adjusting the Kilogram of the Archives in 1779, Fortin employed
a balance sensitive to one part in a million.
As units of capacity are defined in terms either of linear
measures or of mass, the construction of suitable standards does
240 EVOLUTION OF WEIGHTS AND MEASURES
not present any particular difficulty, nor is any high degree of
precision required, save in a few cases. In fact, standard
measures of capacity are usually adjusted by means of the
weight of a liquid such as water, taken at a certain temperature.
As these measures are used in few experiments or determina-
tions where extreme accuracy is called for, there is no need
of observing particular precautions, either in their construction
or their calibration. The standards are usually of some metal,
such as bronze or gun-metal, of a regular geometrical shape,
and are adjusted with water at a certain temperature. The
purpose for which a measure of capacity is to be used is borne
in mind in determining its shape, as with liquids it is not
necessary to take into consideration the question, of compres-
sibility or of heaping the measure which would be involved in
the measurement of grain or vegetables. This, of course, does
not affect the actual cubical contents of the measure, but merely
considers its actual application in commerce. Thus, in Great
Britain there have been various shapes adopted for standards for
the liquid and dry gallon, and for the coal bushel, and for other
measures, the exact dimensions of which are defined. In view
of the great inaccuracy in measuring goods by capacity measures
being unavoidable, it is the present tendency of metrology to
use capacity measures as little as possible, and to recommend
the use of weights, especially in business dealings. In Europe
this practice is rapidly increasing among the metric countries,
and in some of them nearly all articles of food and other
necessities for daily life, even liquids such as oil, are bought and
sold by weight.
There is, however, one kind of standard of capacity where
accuracy is important, namely, flasks, burettes, or other vessels of
glass employed in physical or chemical experiments. These are
calibrated carefully with water or mercury, whose volume at any
specified temperature is known with exactness. Such standards,
however, are not specially and exclusively maintained by national
bureaus and direct comparisons made with them, but as their cali-
bration involves little difficulty to the trained physicist or chemist,1
1 The calibration of chemical and other graduated glass-ware is one of the
regular routine duties of the National Bureau of Standards at Washington, and
is done for the technical public at reasonable and established fees.
STANDARDS AND COMPARISON 241
they are usually constructed in any laboratory where their use
is desired.
In the case of other standards, such as those of electricity, the
most important are the ohm and the standard cell, which involve
the realization of the international definitions1 by careful scientific
work. These definitions for practical purposes are so exact and
the modes of construction so well understood by physicists that
such standards can be constructed at national or other physical
laboratories and bureaus of standards by trained investigators,
and the results represent refined methods of manipulation and the
use of specific apparatus rather than scientific work of such
character as was involved in the construction of the international
standards of length and mass. It should not be understood,
however, that from the purely scientific point of view that
electrical engineers and physicists are altogether satisfied with
the present definitions. Consequently there is at present much
important investigation in progress which has as its object the
determination of new standards or new definitions, and at the
Electrical Congress held at St. Louis in 1904 it was decided that
steps should be taken to form an international electrical com-
mission composed of official representatives, much after the fashion
of the International Commission of Weights and Measures. The
call for a preliminary meeting of delegates has been issued and
the formation of this international commission in the near future
is probable. From the discussion of the electrical units in the last
chapter their independence on each other will be appreciated, so
that it is necessary to determine whether the voltameter operating
under standard conditions shall give the unit of current from
which, with the ohm, may be derived the unit of electromotive
force, or whether the unit of electromotive force as given by a
standard cell shall be considered the fundamental source of the
standards.
There have been constructed by the Physikalisch-Technische
Reichsanstalt at Berlin and the English National Physical
Laboratory, primary mercurial standards of resistance in which
the international definition of the ohm has been realized and
the apparatus of these two laboratories shows substantial
agreement of measurement, being in harmony to a few parts in
1 See chapter ix. ante.
Q
242 EVOLUTION OF WEIGHTS AND MEASURES
IOOjOOO.1 Furthermore there are in England, preserved at the
Board of Trade Electrical Standardizing Laboratory in London,
actual standards of resistance, current and electrical pressure
which have been duly legalized (Order in Council, August 23, 1894).
Thus the standard ohm is the resistance between the copper ter-
minals of the platinum-silver coil marked " Board of Trade Ohm
Standard, verified 1894," to the passage of an unvarying electrical
current, when the coil of insulated wire forming part of the
aforesaid instrument and connected to the aforesaid terminals is
in all parts at a temperature of 15*4 degrees Centigrade.
The standard ampere is the current which passes in and through
the coils of wire of the standard ampere balance, marked " Board
of Trade Ampere Standard, verified 1894," when on reversing the
current in the fixed coils the change in the forces acting upon
the suspended coil in its sighted position is exactly balanced by
the force exerted by gravity in Westminster upon the iridio-
platinum weight marked " A" and forming part of said instrument.
The British standard volt is one-hundredth part of the pressure
which, when applied between the terminals of a Kelvin electro-
static voltmeter of the multicellular type marked " Board of Trade
Standard, verified 1894," causes a certain exactly specified amount
of rotation of the suspended part of the instrument.
While various other standards are of course possessed by the
different national laboratories and testing bureaus, yet they aim
rather at representing specifically the definitions of the various
units, than, as in the case of the British Board of Trade, employing
as national standards the mere concrete apparatus. The same
holds true for standard barometers, thermometers, polariscopes,
and other instruments of precision which are used for standardizing
similar instruments used in science and industry.
Having considered the general principles underlying standards
and their construction and comparison, it may be advantageous to
discuss briefly the weights and measures that have served this
purpose in France and England, as well as the present metric
standards. While it was legally possible to establish the inch by
taking " three barley corns round and dry " as was provided by
the statute of Edward II. and to raise a pound from 7680 grains
xThe first standard ohm was constructed privately by M. Benoit of the
Bureau International.
STANDARDS AND COMPARISON 243
of wheat as was enacted by the statute of the Assize of Bread and
Ale (51 Henry III., stat. 1, 1266), yet such means on their very
face were manifestly lacking in accuracy, as there was nothing to
ensure that the corns or grains would conform to a uniform
standard. Consequently as early as the fourteenth year of the
reign of Edward III. (1340) a royal edict was published ordering
" standard weights and measures to be made of brass, and sent
into every city and town in the kingdom." This necessary and
excellent law, however, merely followed the precedent made by
Eichard I., who ordered that standard measures of length should
be made of iron and that those for capacity should have iron
brims, and that standard measures of every kind should be kept
by the sheriffs and magistrates of towns. While it cannot be
said that this law was enforced, yet it shows that the government
was alive to the necessity of proper standards in order to
secure the desired uniformity and that their construction was
constantly in mind.
The earliest English standard of length extant is the Exchequer
standard yard of Henry VII., which dates back to 1496. It is a
brass bar of octagonal cross section whose length furnished the
standard distance, and which is divided both into inches and also
into sixteen equal parts on the basis of binary division. It was
used until 1588, when in the reign of Queen Elizabeth a new
standard yard, also of brass, was constructed, which is still in
existence after having served for a long period as an original
standard. It is a rectangular bar one yard in length, on which
are indicated the divisions of a yard and also a similar bar forming
an ell of 45 inches (exact length 45*04 inches), there being a
third and larger bar with two beds or matrixes into which both
of the end standard bars could fit, and having at one end of the
yard bed a subdivision into inches and half inches. It may be
said in passing that both the standards of Henry VII. and of
Elizabeth are essentially of the same length, and they are only
about '01 inch shorter than the present British imperial standard.
The Elizabethan standard did duty until well into the nineteenth
century, in spite of the fact that some time between 1760 and
1819 it had been broken and mended by means of a dovetail
joint in a rather crude fashion. In fact this ancient standard has
been spoken of most contemptuously by F. Baily, who examined
244 EVOLUTION OF WEIGHTS AND MEASURES
it in 1836, he even going as far as to call it disgraceful for the
British government to issue certificates and construct copies
based on it as representing the English standard.1
A line standard constructed by Bird in 1760, under the
authorization of the Committee on Weights and Measures of
the House of Commons, was based upon a standard made by
the same maker in 1742 for the Royal Society, and on a line
standard which he constructed in 1758. The former has been
pronounced by H. W. Chisholm, an authority on British
metrology, to be " the first scientifically constructed measure
of length in this country " (England).2 The Bird standard of
1760 was approved by the Committee, and, though not at that
time legally established, formed a basis for a number of
secondary standards. It was eventually adopted as the legal
standard of Great Britain by an Act of Parliament promulgated
June 17, 1824, and served as such until its destruction in the fire
which consumed the Houses of Parliament in 1834. The adop-
tion of this standard, however, at this time was hardly warranted
in view of the state of scientific knowledge, or by the actual
character of the standard itself. It was a brass bar, 1*05 inch
square and 39'73 inches in length, with gold plugs near the ends,
on which were points or dots, the distance between which at the
temperature of 62 degrees Fahrenheit (16*7 degrees Centigrade)
represented the standard yard. This standard bar, however, in
addition to being of comparatively crude construction, even at
the time of its legal adoption had become badly worn by rough
treatment. By the use of beam-compasses, and in various rough
comparisons, the dots had become worn, so that under the micro-
scope they were seen to appear like the craters of small volcanoes,
and consequently rendered the bar quite unsuitable for exact
scientific work. In the Act by which this standard was estab-
lished it is clear that the idea of a natural standard was still
cherished, since it provided that in the event of the loss of
the standard yard it should be restored by means of a reference
1 See H. W. Chisholm, ' ' Seventh Annual Report of the Warden of the Standards, "
1872-3, English Parliamentary Papers, Reports from Commissioners, 1873, vol.
xxxviii. pp. 25 and 34; also id. "Weighing and Measuring" (London, 1877), pp.
50-54. See also footnote, p. 36, ante.
2 See Chisholm in same Report, p. 10, for full description of this and other
standards.
STANDARDS AND COMPARISON
245
to a pendulum beating seconds in a
vacuum, at the latitude of London
and reduced to sea level, which would
have the relation to the yard of
391393 to 36; but in spite of this
statutory provision, when the standard
yard was destroyed ten years later no
recourse was had to the seconds'
pendulum, as that method seemed then
incapable of furnishing the standard
with sufficient exactness, and the stan-
dard yard was reconstructed from other
standards in the possession of the
Government and scientific societies
which had been compared with the
standard of 1760. These included the
five-foot brass standard scale of Sir
George Shuckburgh which was made
by Trough ton, of London, in 1796, two
iron standards made for the Ordnance
Survey in 1826-7, the brass tubular scale
of the Royal Astronomical Society, and
the standard yard of the Royal Society
constructed under Captain Kater's
direction in 1831. The Shuckburgh
scale was based on a five-foot scale
made and used by Troughton, which in
turn was constructed from an accurate
90-inch brass scale made by Bird.1
This imperial standard yard, as well
as the imperial standard prepared
under the direction of a Parliamentary
Committee appointed in 1843, were
xSee W. Harkness, "Progress of Science as
Exemplified in the Art of Weighing and
Measuring," Bulletin, Philosophical Society of
Washington, D.C., vol. x. ; Smithsonian Miscell-
aneous Collection, vol. xxxiii. 1888, pp. 43 et seq.
Present State of the Question of Standards of Length," Proceedings, American
Academy of Arts and Sciences, vol. xv. 1879-80, pp. 273 et seq.
British Imperial Yard.
Also W. A. Rogers, " On the
o
246 EVOLUTION OF WEIGHTS AND MEASURES
duly legalized in 1855 (18 and 19 Vict. c. 72) by an A.ct
known as the Standards Acts, whose provisions as regards
these standards were re-enacted in the Weights and Measures
British Imperial Standard Yard. Cross-section. (Exact size.)
1. — Section of Bar. 2. — Section through holes.
Act of 1878. These standards, as they represent the best
practice of the time of their construction, and as they are
the present standards of Great Britain, may be briefly de-
scribed.1 The imperial standard yard is a solid square bar
of a special bronze or gun-metal known as Baily's metal,
composed of copper 16 parts by weight, tin 2 J, and zinc 1.
Diagram Showing British Imperial Standard Yard from above, a— a=l yard.
It is 38 inches in length, with a cross section one inch square,
and has near its ends two circular holes or wells sunk to a
point midway the depth of the bar. In these wells are inserted
two gold studs, on which the fiducial lines are engraved, the
distance between them forming the imperial standard yard of 36
inches at a temperature of 62 degrees Fahrenheit (16j-° C). This
imperial standard, as also the imperial standard pound, is pre-
served in a strong fire-proof room at the Standards Office in
Old Palace Yard, Westminster, and copies are deposited at
1 G. Airy, ' ' Account of the Construction of the New National Standards of
Length, and of its Principal Copies," Philosophical Transactions (London), 18th
June, 1857.
STANDARDS AND COMPARISON 247
the Royal Observatory, Greenwich, the Royal Mint, the Royal
Society, and the Houses of Parliament. The latter are specially
designated by statute as Parliamentary copies, and must be com-
pared with the imperial standard once in every ten years, since
in the event of the possible destruction of the latter they would
furnish the source from which a new standard would be derived.
There were in addition thirty-five other standards made of the
same size and of the same material, which were duly compared
with the prototype, and were distributed to the various nations of
the world and to scientific institutions in Great Britain and else-
where. One of these standard bars, by Act of Parliament, June
30, 1855, was presented to the United States Government, and
was known as "Bronze Standard No. 11." It is '000088 inch
shorter than Bronze Standard No. 1, which was chosen as the
imperial standard. It was accompanied by a malleable (Low
Moor) iron standard of length, No. 57, and standard weight No. 5,
the correction for each standard being given over the signature of
G. B. Airy, Astronomer-Royal.1
These two yards, particularly the bronze standard, were so
much superior to the Troughton scale that they were accepted
by the United States Office of Weights and Measures as the
standards of the United States, and in this way comparisons
of American measures of length were made with the imperial
yard. In 1876, and again in 1888, they were taken to England
and were compared with the British standards.
In 1904, the late H. J. Chany, Warden of the Standards, caused
to be constructed and standardized at the International Bureau a
platinum-iridium bar similar in composition and section to the inter-
national meter, and while this has not as yet any legal standing,
it is perhaps the best representative of the British yard.
The oldest authenticated British standards of weight date from
the reign of Queen Elizabeth, and consist of three distinct sets.
The first of these are bell-shaped standards of bronze for the
heavier weights, and range from 56 lbs. to 1 lb. inclusive. They
are of importance, as from the time of their construction in 1588
until 1824 they were the standards of the kingdom. Then there
1 See Report, Superintendent U.S. Coast and Geodetic Survey, 1877, Appendix
12, p. 154, for description of these standards of length. See also Executive
Document 27, 34th Congress, 3rd Session, p. 17.
248 EVOLUTION OF WEIGHTS AND MEASURES
is a series of flat circular avoirdupois weights from 8 lbs. to T^
of an ounce, and a set of cup-shaped Troy weights which, with the
exception of the very small weights, fitted into each other. These
standards had been prepared under the direction of a committee
of merchants and goldsmiths, who employed as the basis for
avoirdupois weight a 56 lb. standard of the Exchequer dating from
Edward III., and for Troy weight the
ancient standard of the Goldsmiths' Hall.
About 1758 the Parliamentary Com-
mittee, to which we have before referred,
caused to be constructed three standard
Troy pound weights, but like the yard of
the same period none of these was legalized
until 1824, when one of the weights was
chosen as the government standard, only
to be destroyed by the fire of ten years
later. On the recommendation of the
Standards Committee of Parliament, made
in a report submitted December 21, 1841,
the British imperial standard of weight
was changed from a Troy pound of 5760
grains to an avoirdupois pound of 7000
grains, and a standard representing the-
latter was constructed in 1844 and duly
legalized in 1855. After much discussion
and a careful examination of existing
standards it was found necessary to use
almost exclusively two platinum weights, one belonging to the
Eoyal Society and the other to Professor Schumacher, whose
values were accurately known in terms of the lost standard.
The new standard, which is indeed the present imperial standard,
is of platinum, cylindrical in form, 1*35 inches in height, and
1*15 inches in diameter. Its density as compared with distilled
water is 21*1572, and it displaces *403 grains of air under
standard conditions.1 It has a slight groove or channel near its
upper surface by which it may be moved with a fork of ivory, and
1W. H. Miller, "On the Construction of the New Imperial Standard Pound,
etc.," Philosophical Transactions (London), 1st June, 1856. H. W. Chisholm,.
Weighing and Measuring (London, 1877).
British Imperial Standard
Pound. (Exact size.)
STANDARDS AND COMPARISON 249
bears on its upper surface the inscription "P.S.I 844, 1 lb.," the letters
signifying Parliamentary Standard. Copy No. 5 was presented to
the United States in 1856. The British units of capacity, the
gallon and the bushel, are based on the fact that an imperial
gallon represents the volume occupied by ten imperial pounds of
distilled water at 62 degrees Fahrenheit and a barometric pressure
of 30 inches, while the bushel is eight gallons,1 The imperial
standard gallon bears the date of 1828 and is of brass, with a
diameter equal to its depth. The imperial bushel standard is of
gun-metal, with a diameter twice that of the depth, these latter
dimensions being selected on account of the applicability to the
use for the measure of grain. It dates from 1824, and was
verified in the following year.
The French standard of length previous to the completion of
the Meter of the Archives was the Toise de Perou, to which
reference has already been made. It was constructed for use in
making the base measurements for determining the length of the
Peruvian arc of the meridian and the verification of the arc
passing through Paris, being derived from the Toise du Grand
Chatelet, which dated back to 1668. This latter standard was a
bar of iron which was fixed in the wall of the Grand Chatelet,
forming an inside end standard by which all scales could be tested
by simply placing them between the limiting ends. This naturally
deteriorated from exposure and wear, and, as a result, the Toise
de Perou was substituted for the Toise du Grand Chatelet, as the
French standard of length, in 1766, and is now preserved at the
Observatory in Paris. It is an end standard of polished iron,
somewhat greater than a toise in length and of rectangular
section, 17 lignes in breadth and 4-^ lignes in thickness. At each
end of the bar a rectangular portion extending to a line midway
of the breadth was removed, and the standard distance was taken
between the edges of the remaining portion of the bar, at a point
about one ligne from the median line. On the longer part of the
bar two lines were traced, with points marked at their centers, so
that the distance between them was exactly a toise, with the result
that an end standard was combined in the same metal bar with
the more exact line standard, — there being, however, a difference
1 Henry Kater, "Verification of Standard Gallon," Philosophical Transactions
(London), 1826.
250 EVOLUTION OF WEIGHTS AND MEASURES
between the two scales of about "1 of a millimeter, a quantity
which was readily negligible in the metrology of those days.
The bar was standard at a temperature of 13° Reaumur (16°*25 C.
or 61°'25 F.) and has been found equal to 1-949036 meter at 0° C.
The French standards of weight were a series of weights
known as the Pile of Charlemagne, and dating back to the reign
of that king (about 789). Together they aggregated 50 marcs,
as the unit of the series was termed, or 25 livres poids de marc
(pounds), and in standardizing weights the sum of the pile was
usually taken as the standard. These weights are now preserved
in the Conservatoire des Arts et Metiers at Paris, and have
figured in many comparisons.1
With the experience which the French scientists had gained
in their brilliant geodetic work during the 18th century, it was
possible to employ new and more accurate standards of length
in the measurements of the base lines. Accordingly, for the
purpose of making this fundamental measurement in determining
the length of the earth's quadrant, four compound standard bars
of novel form were designed and constructed by Borda, each
of which was two toises in length, six lignes in width and almost
one ligne in thickness.2 Each bar consisted of a strip of platinum
connected permanently at one end with a strip of copper, which
otherwise was free to move longitudinally as it expanded or
contracted. At the opposite end the copper was cut away for
a short distance and a movable rod of platinum was provided, so
that an exact and variable setting could be made by means of
a divided scale and vernier. As the two metals had unequal
coefficients of expansion, it was possible, by determining their
relative expansion, as indicated by a graduated scale and vernier,
to obtain not only a true measure of length, but also the
temperature of the bar. This was accomplished by first standard-
izing the bars in the laboratory and measuring the relative
expansion corresponding to a certain number of degrees.3 In
1 See C. Mauss, La Pile de Charlemagne (Paris, 1897). A mathematical
discussion of these weights.
2 See Borda, " Experiences sur les regies destinees a la mesure des bases de l'arc
terrestre," Delambre and M^chain, Base du Systeme Me'trique, vol. iii. p. 313.
3 These bars of Borda were studied and standardized by Lavoisier. See Chisholm
in Nature (London), vol. ix. p. 185, Jan. 8, 1874. See also Dumas, Works of
Lavoisier, vol. v.
STANDARDS AND COMPARISON 251
use in the field, these bars were placed end to end and were
carefully levelled. One of them was considered as a standard,
and to this all measurements were referred, including that of
the seconds' pendulum, and when the length of the meter was
evaluated, it was obtained in terms of the fraction ('256537)
of this modulus.1
Compensated bars of this form found increased use in the
measurement of base lines in geodetic surveys until well into
the 19th century, though they have been largely displaced by the
employment of bars of a single material, or steel tapes or wires
whose temperature coefficients are accurately known. In the case
of the metallic bars, in one of the most accurate base measurements
to which reference has already been made, viz., that at Holton,
Mich., which was made in connection with the transcontinental
survey of the United States, the distance was measured by means
of a bar carried in a trough of melting ice.2
In passing from these standards of Borda to the meter, use
was made of the comparator of the Committee, and that of
Lenoir, already described. A provisional standard of brass, first
constructed, served as a means of connecting the two measure-
ments. Finally, when sufficient data had been obtained and
computed to justify the construction of a definite standard, it
was made from a mass of platinum as nearly pure as possible
and of a rectangular section. It was an end standard 4 milli-
meters in thickness and 25 millimeters in breadth becoming the
Meter of the Archives.3 From the same material and at the
same time were constructed two other standards, which differed
only in having a thickness of 35 millimeters. These have since
been known as the Meter of the Conservatory and the Meter
of the Observatory.4
1Benoit, " Dela Precision dans la Determination des Longueurs en Metrologie,"
Rapports presented au Congres International de Physique (Paris, 1900), vol. i.
p. 34. Bigourdan, Le Systeme Metrique (Paris, 1900), p. 83. C. Wolf, " Recherches
historiques sur les etalons des poids et mesures de l'Observatoire," Annales de
I'Observatoire {Memoires), Paris, vol. xvii. p. C 36 et seq.
2 See note ante, p. 141, chapter v.
3 For Cross-section see illustration on p. 252. No. 1 is the Meter of the
Archives.
4C. Wolf, "Recherches historiques sur les etalons des poids et mesures de
l'Observatoire," Annales de V Observatoire (Me'moires), vol. xvii. p. 52.
252 EVOLUTION OF WEIGHTS AND MEASURES
The construction of the actual meter was accomplished by-
using a number of auxiliary rules, which being placed end to
end and compared both among themselves and with the modulus,
enabled the true length of the meter to be obtained. This
proceeding involved considerable careful mathematical work as
well as manipulative skill, and was accomplished with a remark-
able degree of precision, considering the apparatus at the disposal
of the investigators. In fact, it is fair to say that modern work
of this character is more exact only through the improved instru-
ments that an advance in mechanical and scientific knowledge
has made possible, rather than in any greater skill and carefulness
on the part of the observers.
Although a large number of standards of a secondary character
were constructed by the different bureaus established for this
purpose by the French Government as well as by instrument
makers, but little advance was made as regards their form and
general character. In most of them the rectangular shape was
preserved, and though, by the use of the microscope, a more
accurate division was possible, yet no standards of high precision
were attempted. When, however, the custody of the standards
and their verification was assigned to the Conservatoire des Arts
et Metiers, more interest was taken in this work, and with the
installation of new comparators, the scientific staff of that institu-
tion began researches which led to substantial improvements.
It was due to M. Tresca, who was Assistant Director, that a
thorough study of the shape and material of standards was
undertaken, the results of which were placed at the service of
the International Commission, when it assembled in 1870.1
The French Committee, of which he was a member, recom-
mended in preparing the specification for the international meter,
that the new standard should be a line standard, having a cross-
section sufficient in form and dimensions to preserve accurately
the shape of the bar, and that its coefficient of expansion should^
be as nearly as possible that of the meter of the Archives. The
platinum which went to make up this original standard contained
also iridium, together with a small amount of palladium, and
it was deemed desirable, in constructing a new prototype, to
1See Tresca, Appendix 7, Annates du Conservatoire des Arts et Mi '.tiers >
vol. x. 1873.
STANDARDS AND COMPARISON
253
employ an alloy of platinum, with one-tenth part of iridium, as
devised by H. Sainte- Claire Deville, since as such a combination
filled the required conditions of inalterability, homogeneity,
r
R
u
n
H
CI
rj
12
df~ b
Cross-Sections of Standards (Studied by Tresca).
1. — Meter of the Archives. 8. — Provisional Standard of Platinum Iridium.
9, 10, 12.— H Standards. 13, 14, 15.— X Standards.
durability, and small expansibility under the influence of tem-
perature. In addition, it was susceptible of taking a high polish,
and possessed numerous other physical and chemical advantages
which made it particularly suitable for this purpose.1
1 Bigourdan, Le Systeme M&rique, p. 274.
254 EVOLUTION OF WEIGHTS AND MEASURES
In preparing the standards of length, it was realized by the
Commission at the outset that two essential conditions must
be fulfilled, viz., that the metal bars should be as rigid as pos-
sible, without employing such a quantity of the platinum alloy
as would make their cost prohibitive, and, secondly, that the
lines marking the divisions must be placed in the plane of the
neutral fibres. M. Tresca, who had given the subject of
standards careful study, reported to the Commission on their
form, and stated the essentials which must be observed in the
construction of a new standard meter. He called attention to
the fact that it was necessary that the distance between the
two limiting lines should lie entirely in a plane which would
contain the various centres of gravity, and this condition could
only be obtained by making the bar of such cross-section that
it would have the greatest rigidity. He also deemed it essential
that the cross-section should be uniform throughout the length
of the bar, and that the median plane on which the lines were
traced should be available for tracing the necessary divisions,
and for observation with the microscope of the comparator. M.
Tresca carried on a series of experiments and investigations with
bars of different cross-sections for which he calculated the
mechanical constants, and, as a result of the studies, he came
to the conclusion that the most suitable form for the standards
of length was the bar of X section, as shown in the accompany-
ing figures.
«.,, zom™. „ m 2omri m
I I \ Li I I \ Li
1 2
Cross-Section of Standard Meter Bars. (Exact size.)
1.— Line Standard. 2.— End Standard.
It will be seen from the illustration that the median plane,
or plane of the neutral fibres, lies exactly in the center of the
bar, and is available for marking any necessary lines or
divisions. This is the case with the line standard. For the end
STANDARDS AND COMPARISON 255
standard he adopted a somewhat similar section, but with the
cross-bar relatively higher, so that the median plane passed
through its center instead of being situated in its upper surface,
as in the case of the line standard. The section in either case
would be included in a square 20 mm. on each side, and the
diagram represents accurately the actual size and figure of the
section.1
As compared with the Meter of the Archives, the new stan-
dard proposed by Tresca had a profile 1*509 times as great,
so that the actual quantity of material involved was but slightly
more than a third, but the form of construction made possible
far greater strength and rigidity, while at the same time the
standard distance was measured in the neutral plane. These
recommendations were duly adopted, the material was prepared
according to the above specifications, and the bars were delivered
to the Conservatoire des Arts et Metiers, where the standards
were constructed by the French section under the terms of the
international agreement.
In the comparison of the prototype meters among themselves
and with the international standard, the first step was to con-
struct a provisional meter, whose constants were determined
directly in terms of the Meter of the Archives. For this purpose
a comparator with a transverse movement was employed, while
for making the definitive marks on the bars a longitudinal
comparator was used. The comparisons between the Meter of
the Archives and the provisional meter were made at the Conser-
vatoire des Arts et Metiers. The standard bars were taken to the
Bureau International, where was made a series of comparisons
which established their relations to each other, as well as to the
international prototype.2 Of the thirty bars thus examined, the
one that approached most nearly the length of the Meter of
the Archives was selected as the international prototype, and
a new scale was chosen to take its place in the series of
^uillaume, La Convention du Metre (Paris, 1902), pp. 15-18; Benoit, " De
la Precision dans la Determination des Longueurs en Metrologie," JRapports,
Congres de Physique (Paris, 1900), tome i. p. 48.
2 See U.S. Coast and Geodetic Survey Report, 1890, Appendix 18, pp. 743 et seq.y
for a description of the construction of the standard meter bars ; also Bigourdan,
Le Systeme Me'trique.
256 EVOLUTION OF WEIGHTS AND MEASURES
comparisons. As a result of these comparisons, the probable error
of a single comparison was stated at ±0-12 /a — the probable error
in the length of any one of the standards being stated at
±0"04 jii} From the result of many years of comparison at the
Bureau International, the conclusion is reached that the length
of a standard can be absolutely guaranteed to an exactitude of
about *2 micron at all usual temperatures.2
In the construction of standards of weights, the instrument
makers of the eighteenth century had gradually become more
proficient, and their work partook of greater precision, both in
the weights themselves and in the balances. Nevertheless, no
particular features are worthy of note until the kilogram of the
Archives was constructed. This unit of weight, as we have seen,
was defined as the "weight of a cubic decimeter of distilled water,
taken at its maximum density and weighed in a vacuum." To
realize such a definition in a standard would apparently involve
the construction of a cubic vessel whose side was exactly a
decimeter, and then ascertaining the weight of water contained
therein. A measurement of this kind could be made by taking
a vessel of regular form and known interior dimensions, but to
determine its volume accurately by any process of measuring
was a difficult, if not an impossible proceeding. Eecourse was
had, accordingly, to the law of Archimedes, which states that a
body immersed in a fluid loses an amount of weight equal to
the weight of the volume of the fluid which it displaces. Con-
sequently, in order to determine the weight of the displaced
water, it was necessary to weigh a solid body of regular form,
first in air, reducing to vacuum, and then in water, making
suitable provision or correction for its temperature. * In order
to determine exactly the volume of such a body, it must be
constructed in a regular geometric form, such as a cube or a
cylinder. The latter form was adopted in making the standard
of weight by the Committee of the Meter, and Lefevre-Gineau,
with the assistance of Fabbroni, standardized a hollow cylinder
of brass, which was constructed for them by Lenoir. It was
243*5 millimeters in height and diameter, and thus had a volume
1 Benoit, Rapports, Congres International de Physique (Paris, 1900), vol. i.
p. 63.
Ubid. p. 66.
STANDARDS AND COMPARISON 257
slightly in excess of eleven cubic decimeters, and had a weight in
water of about 200 grams.1 The dimensions of the cylinder were
•obtained with a lever comparator from a scale equal to the ^
part of the modulus (the double toise standard of Borda). As a
result of these experiments, a theoretical value of 18827*15 grains
{poids de marc) was assigned to the kilogram, and such a weight
was constructed in pure platinum to be the prototype standard.2
Unfortunately, no record has been left to us of the methods
employed in constructing such a standard. It is known, how-
ever, that at the time when the platinum was prepared for the
four standard meter bars, material was made ready for four
cylinders destined for the standard kilogram. After adjustment,
one of these was taken, and has since survived as the Kilogram
of the Archives. It is unquestionable, however, that the same
balance and weights employed in determining the weight of a
cubic decimeter of water were used in these latter operations.3
During the first half of the 19th century, with the growth
of experimental physics and with improvements of apparatus,
new methods giving a high degree of precision were available for
use with the balance. Consequently, in the construction of
weights and in their reference to standards, much more precision
was obtained than ever previously. This, however, did not cause
any marked demand for new metric standards, although various
physicists were of the opinion that the kilogram did not repre-
sent accurately the mass of a cubic decimeter of water. These
determinations, however, varying as they did — being both greater
and smaller than the Kilogram of the Archives — did not inspire
any greater degree of confidence. Accordingly, when it was
proposed to construct new standards for the meter and the
kilogram, it was decided to use the Kilogram of the Archives
as the basis, and then by subsequent experiments determine
its relation to the mass of a cubic decimeter of water at its tem-
perature of maximum density. Accordingly, the International
Commission made arrangements for such an investigation.
^uillaume, La Convention du Metre, p. 5.
2 For full description of the determination of the standard of mass, see
Delambre and Mechain, Base du Systeme Me'trique, vol. iii. pp. 579-638 ;
Bigourdan, Le Systeme Me'trique, p. 107.
3Bigourdan, Le Systeme Me'trique, p. 159.
R
258 EVOLUTION OF WEIGHTS AND MEASURES
To this body, in 1879, three cylinders of platinum-iridium
alloy, designed for standard kilograms, were delivered, and
were then compressed in a powerful coining-press of the
Paris Mint. They were then given to an instrument maker
for approximate adjustment, and samples of the material were
submitted to chemical analysis by Stas and Sainte-Claire
Deville, it having been found by experiments at the Ecole
Normale that the final density was 21*55. The first adjustment
was made with the kilograms of the Paris Observatory, which
were copied from that of the Archives, and for this purpose
a balance of the Ecole Normale Superieure was employed. After
the three standards had received their final adjustment at the
hands of M. A. Collet, they were then compared with the Kilo-
gram of the Archives, with the standards of the Observatory and
the Conservatoire, and with the standard kilogram of Belgium,,
and then final comparisons were made at the Paris Observatory,
both the French section and the International Committee being
duly represented.1
The volume of these three new standards was determined
by hydrostatic weighings, and compared with that of the standard
of the Archives, which, however, was determined by other methods,
as it was not deemed advisable to place it in water.2 The work
was finished October 18, 1880, when the Committee submitted a
report covering other duties.
After a careful examination of these three kilograms among
themselves, and with the standard kilogram of the Archives, the
committee deemed it wise to select one which was known as
Kill as the standard kilogram, rather than to make a series of
additional comparisons with the other kilograms, to be constructed
as national standards, in the course of which the platinum-iridium
cylinder would doubtless experience a certain amount of injury.
Accordingly, this was adopted in a formal resolution, at a meet-
ing held October 3, 1883, and that kilogram has since been
designated by |Ji, although it bears no mark.3
In the following year, after several attempts had been made to
secure an alloy of the necessary purity, satisfactory material
1 Guillaume, La Convention du Metre (Paris, 1902), p. 123.
2 Ibid. p. 124.
3Bigourdan, Le Systeme Me'trique des Poids et Mesures (Paris, 1901), p. 365.
STANDARDS AND COMPARISON 259
suitable for the national prototypes was delivered in the form of
forty cylinders. These were worked down to approximately the
exact weight, and finished under the direction of the members of
the commission and an elaborate series of comparisons was under-
taken.1
The weighings were effected by means of the Rueprecht and
Bunge balances already described, the latter being employed
when comparisons were made with the international prototype,
which, of course, was preserved most carefully from any deterio-
rating influences. The constants were calculated separately for
each standard, and they were found to agree within a limit of
one milligram, and were accepted by the International Committee,
this decision being formally sanctioned at the International Con-
ference in 1889. Originally it had been determined to insist on
an accuracy of '2 of a milligram for each kilogram, but in certain
cases it was found that the polishing had been carried on too
vigorously, and it was accordingly found necessary to fix the limit
of accuracy at one milligram, within which limits the forty
standards all fell. For example, those given to the United
States, in the drawing by lot (Nos. 4 and 20) were found to have
an error of — '075 milligram and — '039 milligram respectively.2
The permanence of the national standards of mass is no less
important than that of the standards of length. After about
ten years there was made at the Bureau International a com-
parison of eight standards from seven different nations with the
working standards of the Bureau, and it was found that the
deterioration experienced was barely appreciable, ranging as it
did from '027 milligram in the case of one of the Belgian
standards, to '001 of a milligram in the case of that from
Roumania. It was possible that the deterioration in the case
of some of the kilograms which had experienced considerable
usage, was as much as '04 of a milligram, but it was believed that
the future would not show as great an amount of change.3
The idea of the founders of the Metric System to establish a
unit of length which would be absolutely invariable, by means of
its reference to the dimensions of the earth, and also by reference
1Guillaume, La Convention du Metre, p. 125. 2 Ibid. p. 126.
3 Ibid. p. 127. Also Report by M. Benoit in Proces-Verbaux des Seances de
1900, ComiUs International des Poids et Mesures. See also Proces- Verbaux, 1905.
260 EVOLUTION OF WEIGHTS AND MEASURES
to the seconds' pendulum, was not destined to survive. It soon
was seen, in view of subsequent researches, that the trigono-
metrical operations on which the length of the meter was based
were not carried on with an exactitude required by modern
methods of geodetic work, and that, as a result, the standard was
in error by about *1 millimeter. This did not detract from the
usefulness of the system, but it did require the abandonment of
the idea of referring the meter to the ten-millionth of the earth's
quadrant as a natural standard. A century after the Metric
System was established, it was found possible to realize the
condition of reference to a natural and invariable standard, which
was at that time thought so fundamental, and the meter was
defined in terms of wave-length of light, after a series of most
elaborate experiments carried on at the International Bureau of
Weights and Measures by Professor A. A. Michelson, later of the
University of Chicago, who had previously distinguished himself
by his accurate determination of the velocity of light.
The fundamental idea of using a wave-length of light was by
no means new, as a unit of this nature had been proposed by
J. Clerk Maxwell,1 who suggested that a system of absolute
units could be founded on the following basis :
As a unit of length, the wave-length of some determined kind
of light in vacuo,
As a unit of time, the period of vibration of this light,
As a unit of mass, the mass of a single molecule of a specified
substance.
By determining a unit of length in terms of wave-lengths of
light, a standard would be obtained independent of any gradual
contraction of the terrestrial globe, which naturally would produce
a change in the length of the meridian, or other terrestrial
disturbance. Likewise, it would be independent of molecular
changes occurring in a metallic bar, and naturally affecting its
dimensions. The length of a wave of light would under all
conditions be most invariable, as it depends solely on the
elasticity of the ether. Such a unit, then, gives us a means of
establishing the permanent values of the meter, as by determining
its length in these minute distances represented by the vibration
of particles producing one kind of light, we have a much better
1 Maxwell, Electricity and Magnetism (third edition, Oxford, 1891), vol. i. pp. 3, 4.
STANDARDS AND COMPARISON 261
means of fixing its invariability than by comparing it with the
length of a meridian or with the seconds' pendulum.
In order to define the standard of length in terms of the
wave-length of light, a study of different sources of light was
essential, and was carried on by Professor Michelson with great
thoroughness. For this purpose, he used the luminous vapors of
metals produced by the passage of an electric current from the
induction coil through a vacuum tube. By a process of elimina-
tion, he found that the most suitable source of light was the
spectrum furnished by the metal cadmium, which gave a series of
lines valuable for his purpose. The visible spectrum of this
metal consisted of four groups of lines, — one red, which was single
and also fine ; the second, a series of fine green lines ; the third,
a blue line ; the fourth, a violet line. In his early experiments,
Professor Michelson used the green rays, but in later work,
especially by M. Hamy and M. Chappuis, the others were
employed and greater precision was attained.1
Professor Michelson's method is based on the fact that inter-
ference is produced in a beam of light after two of its component
parts are compelled by means of reflection to travel distances
slightly unequal. The earliest application of this principle of
interference in metrology was when Fizeau endeavored to
determine accurately the coefficients of expansion of samples of
various substances. By placing a plano-convex lens over and
very close to the terminal surface of the body to be studied, and
causing a beam of sodium (yellow) light to fall from above on the
lens, he was able to obtain the optical phenomenon known as
interference by observing the reflected beam. This was similar
in nature to the well-known experiment called Newton's rings,
where the difference in path of the rays of light reflected from
the surface of a body and those reflected from the surface of the
lens produces interference. The reason for this is found in the
fact that waves of monochromatic light, when so impeded that a
part of them lose a half-wave length or some odd number of
half-wave lengths, will neutralize each other, and consequently
produce darkness when they reach a certain point. This is due
to the particles at this point being under the influence of waves
in opposite phases. If, on the other hand, where they meet, the
1 Guillaume, La Convention du Metre, p. 147.
262 EVOLUTION OF WEIGHTS AND MEASURES
number of half-wave lengths is even, there is increased effect,
which is manifested by greater brightness. In the case of a lens,
arranged as above, there would be a series of alternate light and
dark concentric rings. If white light is used, these rings will
show spectral colors, which become complex with an increase in
distance from the center. With such an arrangement, Fizeau was
able only to measure short distances, which did not exceed 12 or
15 mm. in length. His method was useful, however, in measuring
accurately the screw of the micrometer of the comparators.1
Using the same idea, but developing it practically, Professor
Michelson was able to measure the length of the meter in terms
of waves of light. Part of the difficulty was solved by the
American physicist when he found a suitable source of light, as
has been described above, but it was largely due to his ingenious
methods and apparatus, as well as to his manipulative skill, that
he was able to carry his plan to so successful a conclusion.2 His
arrangement was, in substance, as follows : Light from the given
source, S, was allowed to fall on a glass plate at A, ground so
that the surfaces were perfectly plane and parallel. This plate
was placed obliquely to the axis of the beam and on the side A
was silvered, so that it formed a semi-transparent reflector. The
beam falling on this silvered surface was divided into two parts,
one of which passed through the silver film and glass, and after
reflection at E in the mirror B to a mirror, Nt from which it
was reflected back through the glass plate to the interior
surface of the film, where it underwent reflection again,
back through the glass and to a telescope, T, so arranged as to
enable the fringes produced in its field to be observed. The other
part of the beam was reflected at the silvered surface and trans-
mitted through a second glass plate, Q, whose thickness was equal
to the first, to a mirror, M, where it was reflected back through
the first plate in the same direction as the first beam. Both
1J. Rene Benoit, "Etudes sur l'appareil de M. Fizeau pour la mesure des
dilatations appartenant au Bureau International des Poids et Mesures," vol. ii.
Travaux et M6moires, Bureau International des Poids et Mesures, Paris.
2 Guillaume, La Convention du Metre (Paris, 1902), pp. 146-169. A. A. Michelson,
"Determination expe>imentale de la valeur du metre en longueurs d'ondes
lumineuses," vol. xi. Travaux et Mdmoires, Bureau International des Poids et
Mesures, Paris.
STANDARDS AND COMPARISON 263
H
A
V
264 EVOLUTION OF WEIGHTS AND MEASURES
beams meeting at the telescope, interference phenomena would
appear if there were any difference in the length of their respective
paths, ADFEFDAC and ABAC. By displacing one of the mirrors
by a small amount through the agency of a screw, this difference
of position could be measured in terms of wave-length. The first
task of the investigator was to determine the length of a very short
standard by displacing the fringes for a counted number of wave-
lengths. Then with this as a standard, he would be able to construct
a standard twice as long and derive its length in wave-lengths. In
this way Professor Michelson prepared a number of standards of
lengths, each double the length of another, so that he was able to
step from one to the other and at the same time preserve the
original accuracy, Finally he standardized a piece one decimeter
in length, and with this he made a comparison with the inter-
national meter, displacing it ten times and measuring the displace-
ment by interference methods so as to start from the first line of
the meter and then reach the second, and so on ; using three
different kinds of light, viz. the red, green, and blue of the
cadmium spectrum, he determined the wave-length of each or
the number of times this wave-length was contained in the
standard meter. The wave-lengths for each color were as
follows :
Red radiations 1 meter =15531 63 '6 \R, of which kR = -64384722 /x.
Green radiations 1 meter = 1966249*7 Xv, of which AF= "50858240 /x.
Blue radiations 1 meter = 2083372-1 XB, of which AB= -47999107 /x.
The accuracy of this work is almost incredible, as the
variation in the measurements was only about one part in ten
million. In fact, where a precision of from one-fourth to
one-fifth of a micron is possible in the case of determining
the relative length of two standards, here is an absolute
measurement which gives the length of a standard in terms
of a natural unit, under conditions reproducible at any time. This,
of course, gives a permanent check on the integrity of the meter,
as in the event of the international prototype being damaged
or destroyed, sufficient data is at hand to enable such physicists
as may be found at any international laboratory or bureau of
standards to redetermine this fundamental unit. The apparatus of
Professor Michelson represented the highest skill of the instrument
STANDARDS AND COMPARISON 265
maker, as mirrors and optical planes were finished to a high
degree of exactitude, reaching in some cases an accuracy as
great as 40^00 of a millimeter, or the -^ of the mean wave-
length of light.
Just what this work of determining standards of length in
terms of the wave-length of light means to science can be readily
understood if a moment's consideration be given to the enormous
mass of scientific and technical literature and knowledge, to the
numberless instruments of measurement and tools and appliances
of trade. At first thought it would seem that if some cataclysm
should suddenly destroy all these evidences of advancement, then
the poor individual who might have survived would be compelled
to begin all over again, and his standards and units would
have to be new, and he would have no means of connect-
ing his system with the past. All the observations on
matters astronomical or terrestrial, all that mass of information
which it has taken centuries and centuries to accumulate, would
be hopelessly lost because of the break in the standards of
measurement. The meter would be gone, the quadrant of the
earth no longer the same, and apparently our last tie broken.
ISTot all the ties, for one, a little one, remains, like hope in the
bottom of Pandora's box. A wave of light so small that a
thousand would scarcely reach across the eye of a needle, this
is the key to the restoration of our system of most complicated
and complete units. So long as the earth has a material exist-
ence, so long as there is light and heat, so long is man in
the position to rebuild his system of units and standards.
The work of Michelson in comparing the international meter
with the wave-lengths of light has put our system upon a
foundation that is as permanent as the universe. If man were
transported to the uttermost confines of the universe, he would
still have the little waves of light, and they would be just the
same as here.
If some day we are able to communicate with the dwellers
upon some other planet, it will be a simple thing to communicate
to them our standard of length and time and mass, and with the
little waves of light to convey our message we may ultimately
impart our exact knowledge to them, and receive theirs in
return. The laws of light motion, of gravitation, of electricity
266 EVOLUTION OF WEIGHTS AND MEASURES
are undoubtedly identical for the whole universe, and given
the first communication of another world we would be
able to establish a truly universal system of units and stan-
dards. By this means inter-planetary communication would
be placed upon a quantitative basis, and the omnipresent, ever-
lasting, but ultra-microscopic wave of light would be the
universal, unchanging standard.
APPENDIX.
TABLES OF CONVERSION FEOM COMMON TO METRIC
MEASURES, USEFUL CONSTANTS AND
EQUIVALENTS.
NOTE.
Unless otherwise specified, the following tables are based
on the U.S. Legal Equivalents. They are derived for the
most part from the Tables of Equivalents published by the
National Bureau of Standards of the U.S. Department
of Commerce and Labor.
LEGAL EQUIVALENTS OF THE UNITED STATES.
Act of July 28, 1866. Revised Statutes 3570.
MEASURES OF LENGTH.
Metric Denominations and Values.
Equivalents in Denominations in Use.
Myriameter,
.
10,000 meters.
6-2137 miles.
Kilometer,
-
1,000 meters.
0-62137 miles or 3,280 feet and 10 inches.
Hectometer,
-
100 meters.
328 feet and 1 inch.
Dekameter,
-
10 meters.
393-7 inches.
Meter,
-
1 meter.
39-37 inches.
Decimeter,
-
y (7 of a meter.
3-937 inches.
Centimeter,
-
y^jTj- of a meter.
0-3937 inch.
Millimeter,
-
ToVo" °f a meter.
0-0394 inch.
MEASURES OF CAPACITY.
Metric Denominations and Values.
Equivalents in Denominations in Use.
Names.
Number
of Liters.
Cubic Measure.
Dry Measure.
Liquor or
Wine Measure.
Kiloliter \
or Stere J
Hectoliter
Dekaliter
Liter
Deciliter
Centiliter
Milliliter
1000
100
10
1
1
TO"
1
TTT0"
TO-TRF
1 cubic meter
YX7 of cubic meter
10 cubic decimeters
1 cubic decimeter
To- cubic decimeter
10 cubic centimeters
1 cubic centimeter
1 -308 cub. yards
/ 2 bushels and \
\ 3 35 pecks J
9-08 quarts
0-908 quart
6 -1022 cub. inches
0-6102 cub. inch
0-061 cub. inch
264-17 gallons.
26-417 gallons.
2-6417 gallons.
1 -0567 quarts.
0-845 gill.
0-338 fluid ounce.
0-27 fluid dram.
MEASURES OF SURFACE.
Metric Denominations and Values.
Equivalents in Denominations in Use.
Hectare,
Are,
Centare,
10,000 square meters.
100 square meters.
1 square meter.
2-471 acres.
119 "6 square yards.
1,550 square inches.
270 EVOLUTION OF WEIGHTS AND MEASURES
WEIGHTS.
Metric Denominations and Values.
Equivalents in De-
nominations in Use.
Names.
Number of
Grams.
Weight of what
Quantity of Water at
Maximum Density.
Avoirdupois Weight.
Millier or Tonneau
Quintal
Myriagram
Kilogram or Kilo
Hectogram
Dekagram
Gram
Decigram
Centigram
Milligram
1,000,000
100,000
10,000
1,000
100
10
1
1
To"
TTTO
1
1 cubic meter
1 hectoliter
10 liters
1 liter
1 deciliter
10 cubic centimeters
1 cubic centimeter
jjy cubic centimeter
10 cubic milliliters
1 cubic milliliter
2204-6 pounds.
220-46 pounds.
22-046 pounds.
2-2046 pounds.
3-5274 ounces.
•3527 ounce.
15*432 grains.
1 -5432 grains.
0-1543 grain.
0-0154 grain.
1000
BRITISH LEGAL (BOARD OF TRADE) EQUIVALENTS.
May, 1898.
LINEAR MEASURE.
Metric.
1 Millimeter (mm. ) (t o~Vo" m- )
1 Centimeter (y^xj m-)
1 Decimeter \y$ m.)
1 Meter (m. )
1 Dekameter (10 m.)
1 Hectometer (100 m.)
1 Kilometer
003937 Ins.
0-3937 Ins.
3-937 Ins.
' 39-370113 Ins.
3-280843 Ft.
. 10936143 Yds.
10-936 Yds.
109-36 Yds.
•62137 Mile.
1 Inch
1 Foot (12 ins.)
1 Yard (3 ft.)
1 Fathom (6 ft.)
1 Pole (54 yds.)
Imperial.
= 25-400 Millimeters.
0-30480 Meter.
0-914399 Meter.
1-8288 Meters.
5-0272 Meters.
1 Chain (22 yds.) = 20-1168 Meters.
1 Furlong
: 201 168 Meters.
1 Mile (8 furlongs) = 1-6093 Kilometers.
BRITISH LEGAL EQUIVALENTS 271
SQUARE MEASURE.
Metric.
1 Square Centimeter = 0*15500 Sq. In.
1 Sq. Decimeter (100 sq. centimeters) = 15*500 Sq. In.
1 Sq. Meter (100 sq. decimeter,) = { ™™ g; ^
1 Are (100 sq. meters) = 119*60 Sq. Yds.
1 Hectare (100 ares or 10,000 sq. meters) = 2*4711 Acres.
Imperial.
1 Square Inch = 6*4516 Sq. Centimeters.
1 Sq. Ft. (144 sq. ins.)= 9*2903 Sq. Decimeters.
1 Sq. Yard (9 sq. ft.) = "836126 Sq. Meter.
1 Perch (30£ sq. yds.) = 25*293 Sq. Meters.
1 Rood (40 perches) = 10*117 Ares.
1 Acre (4840 sq. yds.) = 0*40468 Hectare.
1 Sq. Mile (640 acres) =259 Hectares.
CUBIC MEASURE.
Metric.
1 Cubic Centimeter = '0610 Cubic In.
1 Cubic Decimeter (c.d.) (1000 cubic centimeters) = 61*624 Cubic Ins.
. « . . ., t /1AAA .. , . . > f 35*3148 Cubic Ft.
1 Cubic Meter (1000 cubic decimeters) =■{ nrvf,neA ~ , . «..
I 1*307954 Cubic Yds.
Imperial.
1 Cubic Inch = 16*387 Cubic Centimeter.
1 Cubic Foot (1728 cub. ins.) = 0*028317 Cubic Meter.
1 Cubic Yard (27 cub. ft.) = 0*764553 Cubic Meter.
CAPACITY.
Metric.
1 Centiliter (TJ<j liter) = *670 Gill.
1 Deciliter (TV liter) = *176 Pint.
1 Litre = 1 *75980 Pints.
1 Dekaliter (10 liters) =2*200 Gallons.
1 Hectoliter (100 liters) = 2*75 Bushels.
Imperial.
1 Gill = 1 *42 Deciliter.
1 Pint (4 gills) = *568 Liters.
1 Quart (2 pints) = 1 *136 Liters.
1 Gallon (4 quarts) =4*5459631 Liters.
1 Peck (2 gallons) =9*092 Liters.
1 Bushel (8 gallons) =3*637 Dekaliters.
1 Quarter (8 bushels) = 2*909 Hectoliters.
272 EVOLUTION OF WEIGHTS AND MEASURES
WEIGHT.
Metric.
1 Milligram (iijjyjj grm.) =
1 Centigram (T J^ grm. ) =
1 Decigram (y o grm- ) =
1 Gramme (1 grm.) =
1 Dekagram (10 grm.) —
1 Hectogram (100 grm.) =
1 Kilogram (1000 grm.) =
1 Myriagram (10 kilog.) =
1 Quintal (100 kilog.)
1 Tonne (1000 kilog.)
1 Gramme (1 grm.) =
1 Gramme (1 grm.) ==■
Imperial.
Avoirdupois.
1 Grain :
1 Dram
1 Oz. (16 drams)
1 Pound (16 oz. or 7000 grains) =
1 Stone (14 lb.)
1 Quarter (28 lb.)
1 Hundredweight (cwt.) (112 lb.) = {
lTon(20cwt.)
Troy.
1 Grain
1 Pennyweight (24 grains)
1 Troy ounce (120 pennyweights):
Apothecaries' Weight.
1 Grain :
1 Scruple (20 grains) :
1 Drachm (3 scruples) -.
1 Oz. (8 drachms) :
Avoirdupois.
0-015 Grain.
0-154 Grain.
1 -543 Grains.
15-432 Grains.
5-664 Drams.
3-527 Oz.
f 2-2046223 Lb. oz.
115432-3564 Grains.
22-046 Lb.
1-968 Cwt.
0-984 Ton.
Troy.
/ 0-03215 Oz. Troy,
t 15-432 Grains.
Apothecaries' Weight.
( 0-2572 Drachm.
| 0-7716 Scruple.
I 15-432 Grains.
0-0648 Gramme.
1 -772 Grammes.
28-350 Grammes.
0-45359243 Kilogram.
6 "350 Kilograms.
12-70 Kilograms.
50-80 Kilograms.
0-5080 Quintal.
/ 1-0160 Tonnes or
U016 Kilograms.
0 0648 Gramme.
1 "5552 Grammes.
31-1035 Grammes.
0-0648 Gramme.
1 -296 Grammes.
3-888 Grammes.
31-1035 Grammes.
APOTHECARIES' MEASURE.
1 Minim
1 Fluid Scruple
1 Fluid Drachm (60 minims)
1 Fluid Ounce (8 drachms)
1 Pint
= 0-059 Milliliter.
= 1-184 Milliliters.
= 3-552 Milliliters.
= 2-84123 Centiliters.
= 0-568 Liter.
1 Gallon (8 pints or 160 fluid oz.) = 4-5459631 Liters.
EQUIVALENTS OF UNITS OF LENGTH
273
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COMPARISON OF PRICES
277
COMPARISON OF PRICES.
FRENCH AND GERMAN PRICES FOR METRIC UNITS, BRITISH PRICES
FOR IMPERIAL UNITS, AND UNITED STATES PRICES FOR UNITED
STATES STANDARD WEIGHTS AND MEASURES.
[Based upon the circular of the Secretary of the Treasury dated October 1, 1902,
fixing the legal equivalent of the (German) mark at 23 '8 cents, of the (French)
franc at 19*3 cents, and the British pound sterling at $4 '8665. ]
Francs D°llara
Francs Dollars
Francs D^rs
Francs Dollars
Shillings Dollars
per
per per
meter. yard.
Per $g
llter- liquid gal.
per per
hectoliter, bushel.
per per
British U.S.
imp. gal. liquid gal.
1 = -088
1 = -176
1 = -731
1 = -068
1 = -203
2 = '175
2 = -353
2 =1-461
2 = -136
2 = -405
3 = -263
3 = -529
3 =2-192
3 = -204
3 = -608
4 = -350
4 = -705
4 =2-922
4 = -272
4 = -810
5 - '438
5 = '882
5 =3-653
5 = -340
5 =1-013
6 = -525
6 =1-058
6 =4-384
6 = -408
6 =1-216
7 = '613
7 =1-234
7 =5-114
7 = -476
7 =1-418
8 = '700
8 =1-411
8 =5-844
8 = '544
8 =1-621
9 = -788
9 =1-587
9 =6*575
9 = -612
9 =1-824
11-423=1
5-667 = 1
1-369=1
14-703=1
4-935 = 1
22*846=2
11-334 = 2
2-738=2
29-407=2
9-871=2
34-269 = 3
17-000 = 3
4-106 = 3
44-110 = 3
14-806=3
45-691=4
22-667=4
5-475=4
58-813=4
19-742 = 4
57-115=5
28-334=5
6-844 = 5
73-517=5
24-677=5
68-537=6
34-001 = 6
8-213=6
88-220=6
29-612=6
79-960 = 7
39-668=7
9-581=7
102-923 = 7
34-548=7
91-383=8
45-334=8
10-950=8
117-627=8
39-483=8
102-806=9
51-001 = 9
12-319=9
132-330=9
44-419=9
Marks Walters
Marks Dollars
Marks Do"f8
Marks Dollars
Shillings Dollars
, „ Per avoir
kilogram. pound
per per
meter. yard.
ner per
• U.S
liter- liquid gal.
per per
hectoliter, bushel.
per per
British U.S.
bus. bus.
1 = -108
1 = '218
1 = -901
1 = -084
1 = -236
2 = -216
2 = -435
2 =1-802
2 = -168
2 = -472
3 = -324
3 = -653
3 =2-730
3 = -252
3 = '707
4 = -432
4 = -871
4 =3-604
4 = -335
4 = -943
5 = -540
5 =1-088
5 =4-505
5 = -419
5 =1-179
6 = -648
6 =1-306
6 =5-406
6 = -503
6 =1-415
7 = -756
7 =1-523
7 =6-307
7 = -587
7 =1-650
8 = -864
8 =1-741
8 =7-207
8 = -671
8 =1-886
9 = -972
9 =1-959
9 =8-108
9 = -755
9 =2-122
9-263=1
4-595 = 1
1-110=1
11-923=1
4-241=1
18-526 = 2
9-190=2
2-220 = 2
23-847=2
8-483 = 2
.27-789 = 3
13-785=3
3-330 = 3
35-770 = 3
12-724=3
37-052=4
18-380=4
4*440=4
47-693 = 4
16-965 = 4
46-316 = 5
22-975 = 5
5 550=5
59-616 = 5
21-207 = 5
55-579=6
27-570 = 6
6-660=6
71-540=6
25-448=6
64-842=7
32-165=7
7-770=7
83-463=7
29-689 = 7
74-105=8
36-760=8
8-880=8
95-386=8
33-931 = 8
83-368=9
41-355=9
9-990=9
107-310 = 9
38-172=9
278 EVOLUTION OF WEIGHTS AND MEASURES
LENGTH.
INCHES AND CENTIMETERS.— EQUIVALENTS FROM 1 to 100.
Inches to Centimeters.
Inches to Centimeters.
Centimeters to Inches.
Centimeters to Inches.
0
50
127 000
0
50
19-6850
1
2 540
51
129 540
1
•3937
51
20-0787
2
5-080
52
132 080
2
•7874
52
20-4724
3
7-620
53
134-620
3
1-1811
53
20-8661
4
10-160
54
137-160
4
1-5748
54
21-2598
5
12-700
55
139-700
5
1*9685
55
21-6535
6
15-240
56
142-240
6
2-3622
56
22 0472
7
17-780
57
144 780
7
2-7559
57
22-4409
8
20 320
58
147 320
8
3-1496
58
22-8346
9
22-860
59
149-860
9
3 5433
59
23 2283
10
25 400
60
152-400
10
3-9370
60
23 6220
11
27 940
61
154-940
11
4-3307
61
24-0157
12
30-480
62
157-480
12
4-7244
62
24-4094
13
33 020
63
160020
13
5-1181
63
24-8031
14
35-560
64
162-560
14
5-5118
64
25-1968
15
38-100
65
165-100
15
5-9055
65
25-5905
16
40-640
66
167-640
16
6-2992
66
25-9842
17
43-180
67
170-180
17
6-6929
67
26-3779
18
45-720
68
172-720
18
7-0866
68
26-7716
19
48-260
69
175-260
19
7-4803
69
27-1653
20
50-800
70
177-800
20
7-8740
70
27-5590
21
53 340
71
180-340
21
8-2677
71
27-9527
22
55-880
72
182-880
22
8-6614
72
28-3464
23
58-420
73
185-420
23
9-0551
73
28-7401
24
60-960
74
187-960
24
9-4488
74
29-1338
25
63-500
75
190-500
25
9-8425
75
29-5275
26
66-040
76
193-040
26
10-2362
76
29-9212
27
68-580
77
195-580
27
10-6299
77
30-3149
28
71-120
78
198-120
28
11-0236
78
30-7086
29
73-660
79
200-660
29
11-4173
79
31-1023
30
76-200
80
203-200
30
11-8110
80
31-4960
31
78-740
81
205-740
31
12-2047
81
31-8897
32
81-280
82
208-280
32
12-5984
82
32-2834
33
83-820
83
210-820
33
12-9921
83
32-6771
34
86 360
84
213-360
34
13-3858
84
33-0708
35
88-900
85
215-900
35
13-7795
85
33-4645
36
91 '440
86
218-440
36
14-1732
86
33-8582
37
93-980
87
220-980
37
14-5669
87
34-2519
38
96-520
88
223-520
38
14-9606
88
34-6456
39
99-060
89
226-060
39
15-3543
89
35 0393
40
101-600
90
228-600
40
15-7480
90
35-4330
41
104-140
91
231-140
41
16-1417
91
35-8267
42
106-680
92
233-680
42
16-5354
92
36-2204
43
109-220
93
236-220
43
16-9291
93
36-6141
44
111-760
94
238-760
44
17-3228
94
37-0078
45
114-300
95
241-300
45
17-7165
95
37-4015
46
116-840
96
243-840
46
18-1102
96
37-7952
47
119-380
97
246-380
47
18-5039
97
38-1889
48
121 -920
98
248-920
48
18-8976
98
38-5826
49
124-460
99
251-460
49
19-2913
99
38-9763
LENGTH: FEET AND METERS
279
LENGTH.
FEET AND METERS.— EQUIVALENTS FROM 1 to 100.
Feet
Meters.
Feet
Meters.
Meten
s. Feet.
Meters. Feet.
0
50
15 24003
0
50 164 04167
1
•30480
l
15-54483
1
3-28083
1 167 32250
2
•60960
2
15-84963
2
6-56167
2 170-60333
3
•91440
3
16-15443
3
9 84250
3 173-88417
4
1-21920
4
16-45923
4
13-12333
4 177-16500
5
1-52400
5
16-76403
5
16-40417
5 ISO -44583
6
1 -82880
6
17-06883
6
19-68500
6 183-72667
7
2-13360
7
17 37363
7
22-96583
7 187-00750
8
2-43840
8
17-67844
8
26-24667
8 190-28833
9
274321
9
17-98324
9
29-52750
9 193 56917
10
3-04801
60
18-28804
10
32-80833
60 196-85000
1
3-35281
1
18-59284
1
36-08917
1 200-13083
2
3 65761
2
18-89764
2
39-37000
2 203-41167
3
3-96241
3
19-20244
3
42-65083
3 206-69250
4
4-26721
4
19-50724
4
45-93167
4 209-97333
5
4-57201
5
19-81204
5
49-21250
5 21325417
6
4-87681
6
20-11684
6
52-49333
6 216-53500
7
5-18161
7
20-42164
7
5577417
7 219-81583
8
5-48641
8
20-72644
8
59-05500
8 223 09667
9
5-79121
9
21-03124
9
62-33583
9 226-37750
20
6-09601
70
21-33604
20
65-61667
70 229-65833
1
6-40081
1
21-61084
1
6S -89750
1 232-93917
2
6-70561
2
21-94564
2
72-17833
2 236-22000
3
7-01041
3
22-25044
3
75-45917
3 239-50083
4
7-31521
4
22-55525
4
78-74000
4 242-78167
5
7-62002
5
22-86005
5
82-02083
5 246 06250
6
7-92482
6
23-16485
6
85-30167
6 249 34333
7
8-22962
7
23-46965
7
88-58250
7 252-62417
8
8-53442
8
23-77445
8
91-86333
8 255-90500
9
8-83922
9
24-07925
9
95-14417
9 259-18583
30
9-14402
80
24-38405
30
98-42500
80 262-46667
1
9-44882
1
24-68885
1
101-70583
1 265 74750
2
9-75362
2
24-99365
2
104-98667
2 269 02833
3
10-05842
3
25-29845
3
108-26750
3 272-30917
4
10-36322
4
25-60325
4
111-54833
4 275-59000
5
10-66803
5
25-90805
5
114-82917
5 278-87083
€
10-97282
6
26-21285
6
118-11000
6 282-15167
7
11-27762
7
26-51765
7
121-39083
7 285-43250
8
11-58242
8
26 82245
8
124-67167
8 288-71333
9
11-88722
9
27 12725
9
127 95250
9 291-99417
40
12-19202
90
27-43205
40
131-23333
90 295-27500
1
12-49682
1
27-73686
1
134-51417
1 298-55583
2
12-80163
2
28-04166
2
137-79500
2 301-83667
3
13-10643
3
28-34646
3
141-07583
3 305-11750
4
13-41123
4
28-65126
4
144-35667
4 308-39833
5
13-71603
5
28-95606
5
147-63750
5 311-67917
6
14-02083
6
29-26086
6
150-91833
6 314-96000
7
14-32563
7
29-56566
7
154-19917
7 318-24083
8
14-63043
8
29-87046
8
157-48000
8 321-52167
9
14-93523
9
30-17526
9
160-76083
9 324-80250
280 EVOLUTION OF WEIGHTS AND MEASURES
LENGTH.
YARDS AND METERS.— EQUIVALENTS FROM 1 to 100.
Yards
Meters.
Yards
Meters.
Meter?
Yards.
Meters
Yards.
0
50
45-72009
0
50
54-68056
1
•91440
51
46-63449
1
1-09361
51
55-77417
2
1-82880
52
47-54889
2
2-18722
52
56-86778
3
2 74321
53
48-46330
3
3-28083
53
57-96139
4
3-65761
54
49-37770
4
4-37444
54
59-05500
5
4-57201
55
50-29210
5
5-46806
55
60-14861
6
5-48641
56
51-20650
6
6-56167
56
61-24222
7
6-40081
57
52-12090
7
7-65528
57
62 33583
8
7 31521
58
53-03530
8
8-74889
58
63 42944
9
8-22962
59
53-94971
9
9-84250
59
64-52306
10
9-14402
60
54-86411
10
10-93611
60
65-61667
11
10-05842
61
55-77851
11
12 02972
61
66-71028
12
10-97282
62
56-69291
12
13-12333
62
67-80389
13
11-88722
63
57 60731
13
14-21694
63
68-89750
14
12-80163
64
58-52172
14
15-31056
64
69-99111
15
1371603
65
59-43612
15
16-40417
65
71 08472
16
14-63043
66
60-35052
16
17-49778
66
72-17833
17
15-54483
67
61-26492
17
18-92139
67
73-27194
18
16-45923
68
62-17932
18
19-68500
68
74-36556
19
17-37363
69
63-09372
19
20-77861
69
75-45917
20
18-28804
70
64-00813
20
21-87222
70
76-55278
21
19-20244
71
64-92253
21
22-96583
71
77-64639
22
20-11684
72
65-83693
22
24-05944
72
78-74000
23
21 03124
73
66-75133
23
25-15306
73
79-83361
24
21-94564
74
67-66573
24
26-24667
74
80-92722
25
22-86005
75
68-58014
25
27-34028
75
82-02083
26
23-77445
76
69-49454
26
28-43389
76
83-11444
27
24-68885
77
70-40894
27
29-52750
77
84-20806
28
25-60325
78
71-32334
28
30-62111
78
85-30167
29
26-51765
79
72-23774
29
31-71472
79
86-39528
30
27 43205
80
7315214
30
32-80833
80
87-48889
31
28-34646
81
74-06655
31
33-90194
81
88-58250
32
29-26086
82
74-98095
32
34-99556
82
89-67611
33
30-17526
83
75-89535
33
36-08917
83
90-76972
34
31-08966
84
76-80975
34
37-18278
84
91 -86333
35
32-00406
85
77 72415
35
38-27639
85
92-95694
36
32-91846
86
78-63855
36
39-37000
86
94-05056
37
33-83287
87
79-55296
37
40-46361
87
95-14417
38
34-74727
88
80-46736
38
41 -55722
88
96-23778
39
35-66167
89
81-38176
39
42-65083
89
97-33139
40
36-57607
90
82-29616
40
43 74444
90
98-42500
41
37-49047
91
83-21056
41
44-83806
91
99-51861
42
38-40488
92
84-12497
42
45-93167
92
100-61222
43
39-31928
93
85-03937
43
47-02528
93
101-70583
44
40-23368
94
85-95377
44
48-11889
94
102-79944
45
41-14808
95
86-86817
45
49-21250
95
103-89306
46
42-06248
96
87-78257
46
50-30611
96
104-98667
47
42-97688
97
88-69697
47
51-39972
97
106-08028
48
43 89129
98
89-61138
48
52-49333
98
107-17389
49
44-80569
99
90-52578
49
53-58694
99
108-26750
LENGTH: MILES AND KILOMETERS
281
LENGTH.
MILES AND KILOMETERS.— EQUIVALENTS FROM 1 to 100.
Miles.
Kilometers.
Miles.
Kilometers.
Kilometers. Miles.
Kilometers. Miles.
0
50
80-4674
0
50
3106850
1
1-6093
l
82-0767
1
•62137
l
31-68987
2
3 2187
2
836861
2
1-24274
2
32-31124
3
4-8280
3
85-2954
3
1-86411
3
32-93261
4
6-4374
4
86 9047
4
2-48548
4
33-55398
5
8-0467
5
88-5141
5
3-10685
5
34-17535
6
9-6561
6
90 1234
6
3-72822
6
34-79672
7
11-2654
7
91 -7328
7
4-34959
7
35-41809
8
12*8748
8
93-3421
8
4-97096
8
36-03946
9
14-4841
9
94-9515
9
5 59233
9
36-66083
10
16 0935
60
96-5608
10
6-21370
60
37-28220
1
17 7028
1
981702
1
6-83507
1
37-90357
2
19-3122
2
99-7795
2
7-45644
2
38-52494
3
20-9215
3
101 -3889
3
8-07781
3
39-14631
4
22-5309
4
102-9982
4
8-69918
4
39-76768
5
24-1402
5
104-6076
5
9-32055
5
40-38905
6
25-7496
6
106-2169
6
9-94192
6
41 01042
7
27 3589
7
107-8263
7
10-56329
7
41-63179
8
28-9682
8
109-4356
8
11-18466
8
4225316
9
30-5776
9
111 0450
9
11-80603
9
42-87453
20
32-1869
70
112-6543
20
12-42740
70
43-49590'
1
33-7963
1
114 2637
1
13-04S77
1
44-11727
2
35-4056
2
115-8730
2
13-67014
2
44-73864
3
37-0150
3
117-4823
3
14-29151
3
45-36001
4
38-6243
4
119-0917
4
14-91288
4
45-98138
5
40-2337
5
120-7010
5
15-53425
5
46-60275
6
41-8430
6
122-3104
6
1615562
6
47 22412
7
43 4524
7
123 9197
7
16-77699
7
47-84549
8
45-0617
8
125-5291
8
17-39836
8
48-46686
9
46-6711
9
127 1384
9
18-01973
9
49-08823
30
48-2804
80
128-7478
30
18-64110
80
49-70960
1
49-8898
1
130-3571
1
19-26247
1
50-33097
2
51-4991
2
131-9665
2
19-88384
2
50-95234
3
53-1085
3
133-5758
3
20-50521
3
51-57371
4
54-7178
4
135-1852
4
21-12658
4
52-19508
5
56-3272
5
136-7945
5
21 -74795
5
52 -81 645
6
57-9365
6
138-4039
6
22-36932
6
53-43782
7
59-5458
7
1400132
7
22-99069
7
54-05919
8
61-1552
8
141 -6226
8
23-61206
8
54-68056
9
62-7645
9
143-2319
9
24-23343
9
55-30193
40
64-3739
90
144-8412
40
24-85480
90
55-92330
1
65-9832
1
146-4506
1
25-47617
1
56-54467
2
67-5926
2
148-0599
2
26-09754
2
57-16604
3
69-2019
3
149-6693
3
26-71891
3
57-78741
4
70-8113
4
151-2786
4
27-34028
4
58-40878
5
72-4206
5
152-8880
5
27-96165
5
59 03015
6
74-0300
6
154-4973
6
28-58302
6
59-65152
7
75 6393
7
156-1067
7
29-20439
7
60-27289
8
77-24S7
8
157-7160
8
29-82576
8
60-89426
9
78-8580
9
159-3254
9
3044713
9
61-51562
282 EVOLUTION OF WEIGHTS AND MEASURES
AREAS.
ACRES AND HECTARES.— EQUIVALENTS FROM 1 to 100.
Acres
Hectares.
Acres
Hectares.
Hectares. Acres.
Hectares. Acres.
0
50
20-23436
0
50
123-55220
1
0-40469
l
20-63905
1
2-47104
l
126 02324
2
0-80937
2
21 -04374
2
4-94209
2
128-49428
3
1-21406
3
21 -44842
3
7-41313
3
130-96533
4
1-61875
4
21-85311
4
9-88418
4
133-43637
5
2-02344
5
22-25780
5
12-35522
5
135-90742
6
2-42812
6
22-66249
6
14-82626
6
138-37846
7
2-83281
7
23-06717
7
17-29731
7
140-84950
8
3-23750
8
23-47186
8
19-76835
8
143-32055
9
3-64219
9
23-87655
9
22-23940
9
145-79159
10
4-04687
60
24-28124
10
24-71044
60
148-26264
1
4-45156
1
24-68592
1
27-18148
1
150 73368
2
4-85625
2
25-09061
2
29-65253
2
153-20472
3
5 26093
3
25-49530
3
32-12357
3
155-67577
4
5-66562
4
25-89998
4
34-59462
4
158-14681
5
6-07031
5
26-30467
5
37-06566
5
160-61786
6
6-47500
6
26-70936
6
39-53670
6
163-08890
7
6-87968
7
27-11405
7
42 00775
7
165-55994
8
7-28437
8
27*51873
8
44-47879
8
168 03099
9
7-68906
9
27-92342
9
46 94983
9
170-50203
20
8-09375
70
28 32811
20
49-42088
70
172-97308
1
8-49843
1
28-73280
1
51-89192
1
175-44412
2
8-90312
2
29-13748
2
54 36297
2
177-91516
3
9-30781
3
29-54217
3
56-83401
3
180-38621
4
9-71249
4
29-94686
4
59-30505
4
182-85725
5
1011718
5
30-35154
5
61-77610
5
185-32829
6
10-52187
6
30-75623
6
64-24714
6
187-79934
7
10-92656
7
31-16092
7
66-71819
7
190-27038
8
11-33124
8
31-56561
8
69 18923
8
192-74143
9
11-73593
9
31-97029
9
71-66027
9
195-21247
30
12 14062
80
32 37498
30
74-13132
80
197-6S351
1
1254531
1
32-77967
1
76-60236
1
200 15456
2
12-94999
2
33-18436
2
79-07341
2
202-62560
3
13-35468
3
33-58904
3
81-54445
3
205-09665
4
13-75937
4
33-99373
4
84-01549
4
207-56769
5
14-16405
5
34-39842
5
86-48654
5
210-03873
6
14-56874
6
34-80310
6
88-95758
6
212-50978
7
14-97343
7
35 20779
7
91-42863
7
214-98082
8
15-37812
8
35-61248
8
93-89967
8
217-45187
9
15-78280
9
36-01717
9
96-37071
9
219-92291
40
1618749
90
36-42185
40
98-84176
90
222-39395
1
16-59218
1
36-82654
1
10131280
1
224-86500
2
16-99686
2
37 23123
2
103 78385
2
227 33604
3
17-40155
3
37-63592
3
106-25489
3
229-80709
4
17-80624
4
38-04060
4
108-72593
4
232-27813
5
18 21093
5
38-44529
5
111-19698
5
234-74917
6
18-61561
6
38-8499S
6
113-66802
6
237 22022
7
19-02030
7
39-25466
7
116-13906
7
239-69126
8
19-42499
8
39-65935
8
118-61011
8
242-16231
9
19-82968
9
40 06404
9
121 08115
9
244-63335
CAPACITY : LIQUID QUARTS TO LITERS 283
CAPACITY.
LIQUID QUARTS TO LITERS.— EQUIVALENTS FROM 1 to 100.
Quarts. Liters.
Quarts. Liters.
Liters
Quarts.
Liters.
Quarts.
0
50
47*31793
0
50
52-83409
1
•94636
l
48-26429
1
1-05668
l
53-89077
2
1-89272
2
49-21065
2
2-11336
2
54-94746
3
2-83908
3
50-15701
3
3-17005
3
56 00414
4
3-78543
4
51-10337
4
4-22673
4
57 06082
5
4-73179
5
52-04972
5
5-28341
5
58-11750
6
5-67815
6
52-99608
6
6 34009
6
59-17418
7
6-62451
7
53-94244
7
7-39677
7
60 23086
8
7-57087
8
54-88880
8
8-45345
8
61 -28755
9
8-51723
9
55-83516
9
9-51014
9
62-34423
10
9-46359
60
56-78152
10
10-56682
60
63-40091
1
10-40994
1
57-72788
1
11-62350
1
64-45759
2
11-35630
2
58-67423
2
12-68018
2
65-51428
3
12-30266
3
59-62059
3
13-73686
3
66-57096
4
13-24902
4
60-56695
4
14-79355
4
67 62764
5
14-19538
5
6151331
5
15-85023
5
68-68432
6
15-14174
6
62-45967
6
16-90691
6
69-74100
7
16-08810
7
63-40603
7
17-96359
7
70-79768
8
17-03446
8
64-35239
8
19-02027
8
71-85437
9
17-98081
9
65 29875
9
20-07696
9
72-91105
20
18-92717
70
66-24510
20
21-13364
70
73-96773
1
19-87353
1
67-19146
1
22-19032
1
75-02441
2
20-81989
2
68-13782
2
23-24700
2
76-08109
3
21-76625
3
69-08418
3
24-30368
3
77-13778
4
22-71261
4
70-03054
4
25-36036
4
78-19446
5
23-65897
5
70-97690
5
26-41705
5
79-25114
6
24-60532
6
71-92326
6
27-47373
6
80-30782
7
25-55168
7
72-86961
7
28-53041
7
81-36450
8
26-49804
8
73-81597
8
29-58709
8
82-42119
9
27-44440
9
74-76233
9
3061377
9
83-47787
30
28-39076
80
75-70869
30
31-70046
80
84-53455
1
29-33712
1
76-65505
1
32 75714
1
85-59123
2
30-28348
2
77-60141
2
3381382
2
86-64791
3
31 -22983
3
78-54777
3
34-87050
3
87 '70459
4
32-17619
4
79-49412
4
35-92718
4
88-76128
5
33-12255
5
80-44048
5
36-98387
5
89-81796
6
34-06891
6
81-38684
6
38-04055
6
90-87464
7
35-01527
7
82-33320
7
39-09723
7
91-93132
8
35-96163
8
83 27956
8
40-15391
8
92-98800
9
36-90799
9
84-22592
9
41-21059
9
94-04469
40
37-85436
90
85 17228
40
42-26727
90
95-10137
1
38-80070
1
86-11863
1
43-32396
1
96-15805
2
39-74706
2
87-06499
2
44-38064
2
97-21473
3
40-69342
3
88-01135
3
45-43732
3
98-27141
4
41-63978
4
88*95771
4
46-49400
4
99-32809
5
42-58614
5
89-90407
5
47-55068
5
100-38478
6
43-53250
6
90-85043
6
48-60737
6
101-44146
7
44-47886
7
91-79679
7
49-66405
7
102-49814
8
45-42521
8
92-74315
8
50-72073
8
103-55482
9
46-37157
9
93-68950
9
51-77741
9
104-61150
284 EVOLUTION OF WEIGHTS AND MEASURES
CAPACITY.
GALLONS AND LITERS.— EQUIVALENTS FROM 1 to 100.
Gallons
Liters.
Gallons. Liters.
Liters
Gallons.
Liters
Gallons.
0
50
189 2717
0
50
13-20852
1
3 7854
l
193-0572
1
•26417
l
13-47269
2
7-5709
2
196-8426
2
•52834
2
13-73686
3
11-3563
3
200-6280
3
•79251
3
14-00103
4
15-1417
4
204-4135
4
1 -05668
4
14-26521
5
18-9272
5
208-1989
5
1-32085
5
14-52938
6
22-7126
6
211-9843
6
1 -58502
6
14-79355
7
26 4980
7
215-7698
7
1 -84919
7
15-05772
8
30-2835
8
219-5552
8
2-11336
8
15-32189
9
34-0689
9
223-3406
9
2 37753
9
15-58606
10
37-8543
60
227-1261
10
2-64170
60
15-85023
1
41-6398
1
230-9115
1
2-90588
1
16-11440
2
45-4252
2
234-6969
2
3-17005
2
16-37857
3
49-2106
3
238-4824
3
3-43422
3
16-64274
4
52-9961
4
242-2678
4
3-69839
4
16-90691
5
56-7815
5
246-0532
5
3-96256
5
17-17108
6
60-5670
6
249-8387
6
4-22673
6
17-43525
7
64-3524
7
253-6241
7
4-49090
7
17-69942
8
68-1378
8
257-4095
8
4-75507
8
17-96359
9
71-9233
9
261-1950
9
5 01924
9
18-22776
20
75-7087
70
264-9804
20
5-28341
70
18-49193
1
79 4941
1
268-7658
1
5-54758
1
18-75610
2
83 2796
2
272-5513
2
5-81175
2
19-02027
3
87-0650
3
276-3367
3
6-07592
3
19-28444
4
90-8504
4
280-1222
4
6-34009
4
19-54861
5
94 6359
5
283-9076
5
6-60426
5
19-81279
6
98-4213
6
287-6930
6
6-86843
6
20 07696
7
102-2067
7
291-4785
7
7-13260
7
20-34113
8
105-9922
8
295-2639
8
7-39677
8
20-60530
9
109-7776
9
299 0493
9
7-66094
9
20-86947
30
113-5630
80
302-8348
30
7-92511
80
21-13364
1
117-3485
1
306-6202
1
8-18928
1
21 -39781
2
121-1339
2
310-4056
2
8-45345
2
21-66198
3
124-9193
3
314-1911
3
8-71763
3
21-92615
4
128-7048
4
317-9765
4
8-98180
4
22-19032
5
132-4902
5
321-7619
5
9 24597
5
22-45449
6
136-2756
6
325-5474
6
9-51014
6
2271866
7
140 0611
7
329-3328
7
9-77431
7
22-98283
8
143 8465
8
333-1182
8
10-03848
8
23-24700
9
147 6319
9
336-9037
9
10-30265
9
23-51117
40
151-4174
90
340-6891
40
10-56682
90
23-77534
1
155-2028
1
344-4745
1
1083099
1
24 03951
2
158-9882
2
348-2600
2
11-09516
2
24-30368
3
162-7737
3
352-0454
3
11-35933
3
24-56785
4
166-5591
4
355-8308
4
11-62350
4
24-83202
5
170-3446
5
359-6163
5
11-88767
5
25-09619
6
174-1300
6
363-4017
6
12-15184
6
25 36036
7
177-9154
7
367-1871
7
12-41601
7
25-62454
8
181 -7009
8
370-9726
8
12-68018
8
25-88871
9
185-4863
9
374-7580
9
12-94435
9
26-15288
MASSES : AVOIRDUPOIS POUND AND KILOGRAM 285
MASSES.
AVOIRDUPOIS POUND & KILOGRAM.— EQUIVALENTS FROM 1 to 100.
Pounds
Kilos.
Pounds
Kilos.
Kilos.
Pounds.
Kilos.
Pounds.
0
50
22-67962
0
50
110-2311
1
•45359
l
23 13321
1
2-2046
l
112-4357
2
•90718
2
23-58681
2
4-4092
2
114-6404
3
1-36078
3
24-04040
3
6 6139
3
116-8450
4
1-81437
4
24-49399
4
8-8185
4
119-0496
5
2-26796
5
24-94758
5
11-0231
5
121-2542
6
2-72155
6
25-40118
6
13-2277
6
123-4589
7
317515
7
25-85477
7
15 4324
7
125 6635
8
3-62874
8
26-30836
8
17 6370
8
127-8681
9
4 08233
9
26-76195
9
19-8416
9
1300727
10
4-53592
60
27 21555
10
22 0462
60
132-2773
1
4-98952
1
27 66914
1
24-2508
1
134-4820
2
5-44311
2
28 12273
2
26 4555
2
136-6866
3
5-89670
3
28-57632
3
28-6601
3
138-8912
4
6-35029
4
29 02992
4
30-8647
4
141-0958
5
6-80389
5
29-48351
5
33 0693
5
143-3005
6
7-25748
6
29-93710
6
35-2740
6
145 5051
7
7-71107
7
30-39069
7
37 4786
7
147-7097
8
8-16466
8
30-84429
8
39-6832
8
149-9143
9
8-61826
9
31-29788
9
41-8878
9
152-1189
20
9-07185
70
31-75147
20
44 0924
70
154-3236
1
9-52544
1
32-20506
l
46 2971
1
156-5282
2
9 97903
2
32-65865
2
48-5017
2
158-7328
3
10-43263
3
33 11225
3
50 7063
3
160-9374
4
10-88622
4
33-56584
4
52-9109
4
163 1421
5
11-33981
5
34-01943
5
55-1156
5
165-3467
6
11-79340
6
34-47302
6
57 3202
6
167-5513
7
12-24700
7
34-92662
7
59-5248
7
169-7559
8
12-70059
8
35-38021
8
61-7294
8
171-9605
9
13-15418
9
35-83380
9
63 9340
9
1741652
30
13-60777
80
36-28739
30
66-1387
80
176-3698
1
14-06137
1
36-74099
l
68 3433
1
178-5744
2
14-51496
2
37-19458
2
70-5479
2
180-7790
3
14-96855
3
37-64817
3
72-7525
3
182-9837
4
15-42214
4
3810176
4
74-9572
4
185-1883
5
15-87573
5
38-55536
5
77*1618
5
187 3929
6
16-32933
6
39-00895
6
79-3664
6
189-5975
7
16-78292
7
39 46254
7
81-5710
7
191-8021
8
17 23651
8
39-91613
8
83 7756
8
194-0068
9
17-69010
9
40-36973
9
85-9803
9
196-2011
40
18-14370
90
40 82332
40
88'1849
90
198 4160
1
18-59729
1
41-27691
1
90-3895
1
200-6206
2
19-05088
2
41-73050
2
92-5941
2
202-8253
3
19-50447
3
42 18410
3
94-7988
3
205 0299
4
19-95807
4
42-63769
4
97 0034
4
207 2345
5
20 41166
5
43 09128
5
99-2080
5
209-4391
6
20-86525
6
43 54487
6
1014126
6
211-6437
7
21-31884
7
43-99847
7
103-6172
7
213-8484
8
21 -77244
8
44-45206
8
105-8219
8
216 0530
9
22-22603
9
44-90565
9
108-0265
9
218 2576
286 EVOLUTION OF WEIGHTS AND MEASURES
COMPARISON OF THE VARIOUS TONS AND POUNDS
IN USE IN THE UNITED STATES.
FROM 1 to 10 UNITS.
Long Tons.
Short Tons.
Metric Tons.
Kilograms.
Avoirdupois
Pounds.
Troy Pounds.
•00036735
•00044643
•00073469
•00089286
•00098421
•00041143
•00050000
•00082286
•00100000
•00110231
•00037324
•00045359
•00074648
•00090718
•00100000
•37324
•45359
•74648
•90718
1
■822857
1
1-64571
2
2-20462
1
1-21528
2
2-43056
2-67923
•00110204
•00133929
•00146939
•00178571
•00183673
•00123429
•00150000
•00164571
•00200000
•00205714
•00111973
•00136078
•00149297
•00181437
•00186621
1-11973
1-36078
1 -49297
1-81437
1-86621
2-46857
3
3-29143
4
4-11429
3
3-645S3
4
4-86111
5
•00196841
•00220408
•00223214
•00257143
•00267857
•00220462
•00246857
•00250000
•00288000
•00300000
•00200000
•00223945
•00226796
•00261269
•00272155
2
2-23945
2-26796
2-61269
2-72155
4-40924
4-93714
5
5-76000
6
5-35846-
6
6-07639
7
7-29167
•00293S78
•00295262
•00312500
•00330612
•00357143
•00329143
•00330693
•00350000
•00370286
•00400000
•00298593
•00300000
•00317515
•00335918
•00362874
2-98593
3
3-17515
3-35918
3-62874
6-582S6
6-61387
7
7-40571
8
8
8-03769
8-50694
9
9-72222
•00393683
•00401786
•00492103
•00590524
•006S8944
•00440924
•00450000
•00551156
•00661387
•00771618
•00400000
•00408233
•00500000
•00600000
•00780000
4
4-08233
5
6
7
8-81849
9
11-0231
13-2277
15-4324
10-71691
10-93750
13-39614
16-07537
18-75460
•00787365
•00885786
•89287
•98421
1
•00881849
•009920S0
1
1-10231
1-12000
•00800000
•0090000
•90718
1
1-01605
8
9
907-18
1,000-00
1,016-05
17-6370
19-8416
2,000-00
2,204-62
2,240-00
21-43383
24-11306
2,430-56
2,679-23
2,722-22
1-78571
1-96841
2
2-67857
2-95262
2
2-20462
2-24000
3
3-30693
1-81437
2
2-03209
2-72155
3
1,814-37
2,000-00
2,032-09
2,721-55
3,000-00
4,000-00
4,409-24
4,480-00
6,000-00
6,613-87
4,861-11
5,358-46
5,444-44
7,291-67
8,037-69
3
3-57143
3-93683
4
4-46429
3-36000
4
4-40924
4-48000
5
3-04814
3-62874
4
4-06419
4 53592
3,048-14
3,628-74
4,000-00
4,064-19
4,535-92
6,720-00
8,000-00
8,818-49
8,960-00
10,000-00
8,166-67
9,722-22
10,716-91
10,888-89
12,152-78
4-92103
5
5-35714
6-90524
6
5-51156
5-60000
6
6-61387
6-72000
5
5-08024
6-44311
6
6-09628
5,000-00
5,080-24
5,443-11
6,000-00
6,096-28
11,023-11
11,200-00
12,000-00
13,227-73
13,440-00
13,396-14
13,611'H
14.5S3-33
16,075-37
16,333-33
6-25000
6-88944
7
7-14286
7-87365
7
7-71618
7-84000
8
8-81849
6-35029
7
7-11232
7-25748
8
6,350-29
7,000-00
7,112-32
7,257-48
8.000-00
14,000-00
15,432-36
15,680-00
16,000-00
17,636-98
17,013-89
18,754 60
19,055-56
19,444-44
21,433-83
8
8-03571
8-85786
9
8-96000
9
9-92080
10-08000
8-12838
8-16466
9
9-14442
8,128-38
8,164-66
9,000-00
9,144-42
17,920-00
18,000-00
19,841-60
20,160-00
21,777-78
21,875-00
24,113-06
24,500-00
MEASURES OF CAPACITY
287
MEASURES OF CAPACITY.
EQUIVALENTS FROM 1 to 10.
Milli- U.S.
liters. Liquid
(c.c.) Ounces.
(c-c,) Drams.
U.S.
Apothe-
caries'
Scruples.
Milli-
liters,
(c.c.)
U.S.
Liquid Liters.
Quarts.
U.S.
Liquid Liters.
Gallons.
1 =0-03381
1 =0-2705
0-8115 =
1
1 =0-94636
0-26417= 1
2 =0-06763
2 =0-5410
1
1-2322
1-05668=1
0-52834= 2
3 =0-10144
3 =0-8115
1-6231 =
2
2 =1-89272
0-79251= 3
4 =0-13526
3-6967=1
2
2-4645
2-11336=2
1 = 3-7S543
5 =0-16907
6 =0-20288
7 =0-23670
8 =0-27051
9 =0-30432
4 =1-0820
5 =1-3525
6 =1-6231
7 =1-8936
7-3934=2
2-4346 =
3
3-2461 =
4
4-0577 =
4-8692 =
3
3-6967
4
4-9290
5
6
3 =2-83908
3-17005 = 3
4 =3-78543
4-22673=4
5 =4-73179
1-05668= 4
1-32085= 5
1-58502= 6
1-84919= 7
2 = 7-57087
29-574=1
8 =2-1641
5
5-6S07 =
6-1612
7
5-28341=5
2-11336= 8
59-147=2
9 =2-4346
6
7-3934
6 =5 67815
2-37753= 9
8S-721 = 3
11-0901 = 3
6-4923 =
8
6-34009=6
3 =11 -3563a
118-295=4
14-7869=4
7
8-6257
7 =6-62451
4 =15-14174
147-869=5
18-4836=5
7-3038 =
9
7-39677=7
5 =18-92717
177-442=6
22-1803=6
8
9-8579
8 =7-5708S
6 =22-71261
207-016=7
.25-8770=7
9
11-0901
8-45345=8
7 =26-49804
236-590=8
29-5737=8
9 =8-51723
8 =30-28348
266-163 = 9
33-2704 = 9
9-51014=9
9 =34-06891
U.S.
Dry Liters.
Quarts.
Pack's. Liters-
Deka-
liters.
U.S.
Pecks.
U.S. Hecto-
Bushels. liters.
U.S. Hectolitres
Bushels per
per Acre. Hectare.
0-9081=1
0-11351= 1
0-8S10 =
1
1 =0-35239
1 =0-S707S
1 =1-1012
0-22702= 2
1
1-1351
2 =0-70479
1-14840 = 1
1-8162=2
0-34053= 3
1-7620 =
2
2-83774 = 1
2 =1-74156
2 =2-2025
0-45404= 4
2
2-2702
3 =1-05718
2-29680 = 2
2-7242=3
3 =3-3037
3-6323=4
4 =4-4049
4-5404=5
5 =5-5061
0-56755= 5
0-68106= 6
0-79457= 7
0-90808= 8
1 = 8-80982
2-6429 =
3
3-5239 =
4
4-4049 =
5
3
3-4053
4
4-5404
5
5-6755
4 =1-40957
5 =1-76196
5-67548=2
6 =2-11436
7 =2-46675
3 =2-61233
3-44519=3
4 =3-48311
4-59359=4
5 =4-353S9-
5-4485 = 6
6 =6-6074
6-3565=7
7 =7-7086
7-2646 = 8
1-02157= 9
2 =17-61964
3 =26-42946
4 =35-23928
5-2859 =
6
6-1669 =
7
7-0479 =
6
6-8106
7
7-9457
8
8 =2-81914
8-51323=3
9 =3-17154
11-35097=4
5-74199=5
6 =5-22467
6-S9039=6
7 =6-09545
8 =8-8098
5 =44-04910
7-9288 =
9
14-18871 = 5
8 =6-96622
8-1727 = 9
6 =52-85892
8
9-0808
17-02645=6
8-03879=7
9 =9-9110
7 =61-66874
9
10-2159
19-S6420=7
9 =7-83700
8 =70-47856
22-70194=8
9-18719=8
9 =79-28838
25-53968=9
10-33558=9
288 EVOLUTION OF WEIGHTS AND MEASURES
MEASURES OF MASS.
EQUIVALENTS FROM 1 to 10.
Grains.
Grams.
Avoir-
dupois
Ounces.
Grams.
Ounces. Grams-
Avoir- Kilo-
dupois _ZZfI
Pounds. ^ams-
Troy Kilo-
Pounds, grams.
1
= 0-06480
0-03527 =
1
0-03215= 1
1 =0-45359
1 =0-37324
2
= 0-12960
0-07055 =
2
0-06430= 2
2 =0-90718
2 =0-74648
3
= 0-19440
0-10582 =
3
0-09645= 3
2-20462=1
2-67923 = 1
4
= 0-25920
0-14110 =
4
0-12860= 4
3 =1-36078
3 =1-11973
5
= 0-32399
0-17637 =
5
016075= 5
4 =1-81437
4 =1-49297
6
= 0-38879
0-21164 =
6
0-19290= 6
4-40924=2
5 =1-86621
7
= 0-45359
0-24692 =
7
0-22506= 7
5 =2-26796
5-35846 = 2
8
= 0-51839
0-28219 =
8
0-25721= 8
6 =2-72155
6 =2-23945
9
= 0-58319
0-31747 =
9
0-28936= 9
6-61387=3
7 =2-61269
15-4324
= 1
1
28-3495
1 = 31-10348
7 =3-17515
8 =2-98593
30-8647
= 2
2
56-6991
2 = 62-20696
8 =3-62874
8-03769 = 3
46-2971
= 3
3
85-0486
3 = 93-31044
8-81849=4
9 =3-35918
31-7294
=4
4
113-3981
4 =124-41392
9 =4-08233
10-71691=4
77-1618
=5
5
141-7476
5 =155-51740
11-02311=5
13-39614=5
92-5941
=6
6
170-0972
6 =186-62088
13-22773=6
16-07537=6
108-0265
= 7
7
198-4467
7 =217-72437
15-43236=7
18-75460=7
123-4589
=8
8
226-7962
8 =248-82785
17-63698=8
21-43383=8
138-8912
= 9
9
255-1457
9 =279-93133
19-S4160=9
24-11306=9
APOTHECARIES' AND METRIC WEIGHT
289
£
s
5
<
s
M
«
S
O
5
0
3
0
2
s
«s<
to
J
5s
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P5
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£: oo
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co oo
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co S3
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Sg
00
CO 00
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CO t~
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CO ^
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2 §
c- o
CO
CO to
9 o
Ol oo
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ICO
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2 s
CM 2
co £
i §
• l*«
oi p
8.p
8.1
oi S
3 5
o
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0 rH
01 00
SS8
§ 3
Pico
CO O
O rH
O 00
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9|«
co 3
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5 51
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3 >#
rj< OS
CO
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"* 00
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<* 00
IO 00
• IrH
3d
290 EVOLUTION OF WEIGHTS AND MEASURES
TABLE GIVING
DENSITY (SPECIFIC GRAVITY), MELTING POINT
AND BOILING POINT
MISCELLANEOUS ELEMENTS AND SOLIDS.
Density.
Melting Point.
Centigrade.
Boiling Point.
Centigrade.
Aluminium
Amber
Antimony -
Asbestos -
Asphaltum
Bismuth ■
Bone
Brass
Bronze
Butter
Cadmium -
Calcite
Chalk
Cobalt
Constantan
Copper
Cork-
Feldspar -
German silver -
Glass, common -
,, plate, crown -
,, flint, light
,, ,, heavy -
Gold --- -
Granite
Graphite -
Gutta percha -
Gypsum -
Ice ....
Iron, cast -
,, wrought -
,, wire
,, cast steel
Ivory
Lard -
Lead -
Lime, burned -
Magnesium
Manganese
Manganin -
Marble
Mica - - - .
Nickel
Paraffin
Platinum -
Porcelain -
Potassium -
Quartz
Rubber, unvulcanised
,, hard -
2-60— (270)
1-078
6-71
2-0—2-8
1-07—1-2
9-8
1-7—2-0
8-1—8-6
8-7
0-86
8-6
2-7
2-25—2-69
8-6
8-8
8-5—8-9
0-2
2-55
8-5
2-50—2-70
2-45—2-72
3-15—3-4
3-6-3-9
19-2—19-3
2-5—2-9
1-8—2-24
0-96—0-98
2-32
0-9167
7-1—7-7
7-8
7-7
7-8
1-9
0-93
11*3
2-3—3-2
1-7
7 4
8-4 •
2-65-2-8
2-65—2-93
8-8—8-9
0-87
21-4—21-5
2-2—2-5
0-87
2-65
0-92-0-95
1*2
600-850
425—450
267—268
900—920
31—315
315—320
1500—1800
1000—1150
1000
800
to
1400
1065
0
1200—1400
1300—1400
41—42
325—327
630
1900?
1450—1600
38—56
1800
62
2000
1400— 1700
1400—1700
760-770
100
1450—1600
About 1100
350— 430
687—731
MISCELLANEOUS ELEMENTS AND SOLIDS 291
MISCELLANEOUS ELEMENTS AND SOLIDS— Continued.
Density.
Melting Point.
Centigrade.
Boiling Point.
Centigrade.
Sandstone -
Serpentine
Silver
Slate -
Sodium
Spermaceti
Sulphur
Tallow, beef -
,, mutton
Tin -
Wax, Japanese
,, white
,, yellow
Wood, beech
, , box
,, elm
, , oak
,, poplar -
yellow pine
Zinc
2 2— 2 5
2-4—2-7
10-5
2-6-2-7
0-98
0-8S— 0-94
2 07
0-97
0-92
7 3
0-99
0-96—0-97
0-96-0-97
0-85
1-33
0-80
0-7—0-8
0-40
0-66
715
960
95-6—97-6
44
114
43
47—50
227—232
54
63
62
412—420
740
448
1450—1600
930—950
LIQUIDS.
Acid, hydrochloric -
1-24
,, nitric -
1-42
,, sulphuric
1-84
Alcohol, ethyl -
0-7911
-130
78-3
,, methyl, wood
0-80
66
Amyl acetate -
0-90
140
Aniline, oil
1-02
185
Benzol,
0-881
5
80-3
Carbon di sulphide -
1-265
-113
46
Chloroform ....
1-53
-70
61-2
Ether, sulphuric
0-717
-118
34-9
Glycerine -----
1-24—1-26
-20
290
Mercury -----
13 596
-38-8
357
Oil, linseed -
0 93
,, olive
0-91
Petroleum, crude
1-75—1-84
,, refined -
0-84
,. rhigolene
0-65—0-66
40—70
,, gasolene -
0-66—0-69
70—90
,, benzene -
0-69 -0-70
90—110
Phenol, carbolic acid
1-08
40
180
Turpentine, oil -
0-87
GASES.
Air
0-001293
-200
Carbonic acid -
1865
-57?
- 78 to - 80
Hydrogen -----
0901
-250
-256
Nitrogen -----
1251
-203 to -214
-194
Oxygen
1429
- 181 to - 184
Water vapor -
0804
0
100
292 EVOLUTION OF WEIGHTS AND MEASURES
THERMOMETER SCALES.
CENTIGRADE AND FAHRENHEIT EQUIVALENTS.
For Absolute Temperatures add 273° to Centigrade Scale.
Centigrade.
Fahrenheit.
Remarks.
Centigrade.
Fahrenheit.
Remarks.
-273
-549-4
' ' Absolute zero. "
-6-1
21
-250
-418
Hydrogen boils.
-6
212
-200
-328
Temp, liquid air.
-56
22
-190
-310
Nitrogen boils.
-5
23
-180
-292
Oxygen boils.
-4-4
24
-170
-274
-4
24-8
-160
-256
-39
25
-150
-238
- 3 3
26
-140
-220
-3
26 6
-130
-202
Alcohol freezes.
-2-8
27
-120
-184
-22
28
-110
-166
-2
28-4
-100
-148
-1-7
29
-80
-112
Carbonic acid gas
-1-1
30
-60
-76
boils.
-1
30-2
-40
-40
Mercury melts.
-06
31
-30
-22
Ammonia boils.
0
32
Water freezes.
-25
-13
06
33
-20
-4
1
33-8
-19
-22
1-1
34
-18
-0-4
1-7
35
-17'8
0
2
35-6
-17 2
1
2 2
36
-17
1-4
2-8
37
-16-7
2
3
37 4
-161
3
3 3
38
-16
3 2
3 9
39
-15-6
4
4
39-2
Maximum density
-15
5
4-4
40
of water.
-14-4
6
5
41
-14
6-8
5 6
42
-13-9
7
6
42-8
- 13\3
8
61
43
-13
8-6
6 7
44
-12-8
9
7
44 6
-122
10
7-2
45
-12
10-4
7-8
46
-11*7
11
8
464
-li-i
12
8-4
47
-11
122
8-9
48
-10-6
13
9
48-2
-10
14
9 5
49
-94
15
10
50
-9
15-8
106
51
-8-9
16
11
51-8
-8-3
17
11-2
52
-8
17'6
11-7
53
-7'8
18
12
53-6
-7'2
19
12-3
54
-7
19-4
12-8
55
-6-7
20
13
55-4
THERMOMETER SCALES
293
THERMOMETER SCALES.
CENTIGRADE AND FAHRENHEIT EQUIVALENTS.
For Absolute Temperatures add 273° to Centigrade Scale.
Centigrade.
Fahrenheit.
Remarks.
Centigrade.
Fahrenheit.
Remarks.
133
56
33
91-4
13-9
57
33 3
92
14
57 2
33-9
93
14-4
58
34
93 2
15
59
34-4
94
Ether boils.
15'6
60
35
95
16
60-8
35 6
96
16-1
61
36
96-8
167
62
36-1
97
17
62 6
36-7
98
172
63
37
98-6
Human blood tem-
17-8
64
37 2
99
perature.
18
64 4
37-8
100
18-3
65
38
100-6
18-9
66
38-3
101
19
66-2
38-9
102
19-4
67
39
102-4
20
68
Proper room tem-
39-4
103
20-6
69
perature.
40
104
21
69-8
43 3
110
211
70
45
113
21-7
71
48 9
120
22
71'6
50
122
22 2
72
54 4
130
22-8
73
55
131
23
73-4
60
140
Chloroform boils, 62*.
23-3
74
65
149
Potassium melts, 62°.
23 9
75
65-6
150
Methyl alcohol bis., 66*.
24
75 2
70
158
Woods alloy melts, 65°.
24 4
76
71-1
160
25
77
75
167
25-6
78
76-7
170
26
78-8
80
176
Ethyl alcohol boils, 79°.
26-1
79
82-2
180
26-7
80
85
185
27
80-6
87-8
190
27 2
81
90
194
27-8
82
93-3
200
28
82-4
95
203
Sodium melts, 96°.
28-3
83
98-9
210
28-9
84
99
210-2
29
84-2
99-4
211
29-4
85
100
212
Water boils, under
30
86
125
257
76 cm. pressure.
30 6
87
150
302
31
87'8
Critical tempera-
175
347
311
88
ture of carbonic
200
392
Solder melts, 183°.
317
89
acid.
250
482
Tin melts, 227°.
32
89-6
300
725
Lead melts, 335°.
32-2
90
350
662
Mercury boils,
32-8
91
400
752
357° 3.
294 EVOLUTION OF WEIGHTS AND MEASURES
MISCELLANEOUS CONSTANTS AND EQUIVALENTS.
tt = 3*1416. tt2 = 9*8696. 1/tt = 0"31831. 4tt= 12*566.
1/4*- = 0*07958. Jog7r= -49715. log tt2= -99430. log l/7r=f*50285.
log 4tt= 1-09921. log 1/4tt = 2*90079.
Base of the natural system of logarithms, e = 2*7183, log e= -43429 (Briggs).
Modulus „ „ „ M= l/loge = 2-3026, log M= -36222 (Briggs).
Radian = angle where the arc equals the radius = 57° '2958 = 3437' '75 = 206265".
log radian (in degrees) = 1 "75812, (in minutes) = 3 "53628,
(in seconds) = 5 "31443.
Steradian = the solid angle at the center of a sphere of unit radius which is sub-
tended by the unit area. Total angle at a point equals Air steradians.
Earth's radius in kilometers —
equatorial = 6378 "2, polar = 6356 "5, mean = 6367 "4,
log equatorial = 3 "80469, log polar = 3 "80321 , log mean = 3 "80396.
Mean solar year = 365 "2422 days = 8765 "8 13 hours = 525948 "8 min. =31556928 sec.
Stellar day is 3 min. 55 "9 sec. shorter than the mean solar day, =0*99727 day.
Velocity of sound in dry air at 0°C. is 331 meters per second.
Coefficient of expansion of gases = 1/273 = *003665.
Acceleration of gravity at poles = 983 *2 ; at equator = 978 *0 ; at 45° = 980 *6 ; at New
York = 980*2 ; at Greenwich = 981*2 ; at <f>° latitude = 978(1 +0*0052 sin20).
1 gram of water 1°C. = minor calorie = 4*2 x 107 ergs = 4 "2 joules.
Latent heat of water = 80; of steam = 539.
Specific, heat of air at constant pressure = 0 "237. Ratio of specific heats =1*40.
Capillary constant of water = 7 "7, of alcohol = 2 "3, of mercury = 50 rng./mm.
Velocity of light in vacuo = 3 x 1010 cm. /sec.
Wave length of sodium light = 0 "0005893 mm.
Length of the meter in wave lengths of red cadmium light = 1553163 "5.
1 ampere of current deposits 1 "118 mgr. of silver per second = 0"1740c.c. (H. and 0. ).
A plate of quartz 1 mm. thick at 18° C. rotates the plane of polarization 21° '71.
Ohm = resistance of a column of mercury 1 sq. mm. cross-section, 106 "3 cm. long.
E.M.F. of Latimer Clark cell at 18° is 1-434, of cadmium (Weston) cell at 4° is
1-0190.
The solar constant = 3 gram-calories per sq. cm. per minute.
The mass of the hydrogen atom is = 10-24 gram ; of the electron is = 10-27 gram.
Value of e/m = 4*5 x 1017 electrostatic = 1 *5 x 107 electromagnetic.
Velocity of the electrons — beta particles = 2-7 x 1010, alpha particles = 3 x 109.
Probable speed of a molecule of oxygen at 0° C. =376*6 m./sec. , of hydrogen = 1500*9.
Mean free path of a molecule of air at a pressure of 76 cm. and at 0° C. =9*6 x 10~6.
Number of molecules of air in a c.c. at 0° C. and 76 cm. =6 x 1019.
One atmosphere pressure = 76 cm. of mercury =1*0132 megadynes per sq. cm.
A knot is a speed of one nautical mile per hour =1*1515 statute miles or 1S53'25
meters per hour.
A miner's inch of water is from 1*20 to 1*76 cu. ft. per min. =0*708 liter per sec.
Ratio of the probable error to the mean error is 0*6745 (2/3).
Light year is the distance travelled by light in one year = 9*467 x 1012 kilometers
= 5*8825 x 10» miles.
INDEX.
PACE
Abbot. Gen. Henry L. - - 21 1
Abraham 4, 19
Absolute measurements - - 204
Absolute system - 200
Academy of Sciences, Paris, 47, 48, 65
Academy of Sciences, Paris, Sup-
pression of - - - - 52
Academy of Sciences, National,
U.S. - - - 127, 129, 210
Academy of Sciences, St. Peters-
burg 71
Acts of Congress
119, 121, 127, 128, 129, 131, 132, 210
Actus - - - - - - 26
Adams, John Quincy
109, 115, 116, 117, 118
Aeginetan talent and mina - 27, 28
Airy, Sir G. B. - - - 100, 247
Ale gallon 35
Alexandrian talent - - 25, 32, 33
Alloys, Nickel steel - - - 221
Amenoemopht ... - 22
American Geographical and Statis-
tical Society - - - - 125
American Metrological Society - 129
Ampere - 206, 207, 208, 209, 211
Amphora 28
Angle, Measurement of - - 2< 12
Anglo-Saxon measures of length - 36
Angular acceleration - - - 202
Angular velocity - - - - 202
Anti-Metric argument of American
Society Mechanical Engineers
145-162
Apothecaries' pound 32
Ar 142
Arabs, Measures of - - 29, 38
Arago 100
Arbitrary units - - - - 5
Arbuthnot 10
Arc of Meridian, Measurement of 55
Archinne 94
Are 54
Argentine confederation - - 76
Ark, Dimensions of - - - 11
Aroura - - - - 20, 23
Arpent 45
Articles of confederation, Weights
and measures in - - - 109
As, Roman unit of weight - - 26
Assize of bread and ale 32, 35, 242
Association geodesique - - 71
Assyrian documents, Measures
in 16
Astronomy, Babylonian - - 12
Ater 23
Athena, Temple of 25
Athenian talent 27
Attic foot 25
Aulne, Derivation of - - - 26
Aune des marchands - - - 38
Aune of Paris - - - - 38
Aune, Swiss 97
Australia and the metric system - 102
Austria adopts metric system - 90
Austria- Hungary signs metric
treaty 75
Autun, Talleyrand, Bishop of - 46
Avoirdupois pound
33, 34, 35, 122, 123, 248
Babylonia, Measures of 8, 9, 11, 12, 13,
14, 15, 16, 17, 18, 19, 22
Bache, Professor A. D. 122, 123, 124
Baden adopts decimal measures - 82
Baily, F. - - - - 231, 243
Balance - 24, 236, 237, 238, 239
Baldwin locomotive works - - 188
Bancroft, George - - - - 125
Barcelona - - - - 49, 56
Barker, Geo. F. - - - - 211
Barley corn as a unit - - - 8, 29
Barnard, Prof. F. A. P. - - 129
Barus, Carl 211
296
INDEX
Base measurement
PAGE
- 55
Bassot
- 41
Bath
- 20
Beal
6
Belgic foot -
- 31
Belgium adopts metric system
- 91
Belhaven and Stenton, Lord 101
Benoit, J. Rene - - 69, 219, 251
Berthollet - - - - 54, 99
Bessel 40, 223
Bigourdan, M. - - - 41
Binary subdivision - - - 179
Bird standard .... 244
Bismer-pund 96
Black cubit 29
Blaine, James G. - - - - 159
Board of Trade British specifica-
tions 215
Board of Trade electrical stan-
dards 242
Body measures 6
Boeckh - - - - 11, 29, 30
Boisseau 66
Borda - - - 47, 48, 54, 250, 251
Brandis, J. 11
Brazil and metric treaty - - 75
Briggs, Ernest B. - - - 187
Brighton railway, England - - 168
Brisson 54
British Association committee on
units - - - 205, 207
British Association unit of resist-
ance 207
British engineers in Egypt - - 92
British imperial gallon - - 36
British imperial standards
245, 246, 247, 248, 249
British imperial standard yard - 246
British pharmacopoeia - 192, 197
British standards of length and
weight - 245, 246, 247, 248, 249
British Weights and Measures
Association - 163
Brix 69
Bronze standard No. 11 - - 247
Brumaire 53
Brumer comparator - - - 234
Bunge balance ... - 238
Bureau International des Poids et
Mesures established - - 76
Bureau of Standards, U.S. - 131, 132
Cadmium spectrum, Lines of - 261
Calendar, French reforms in 52, 53
Caliph-Al-Mamum 29
Calipers for standards of length
224, 229
Canaan, Civilization of - - 19
Capacity, Electrical - - 203, 209
Capacity, Measures of
5, 27, 28, 35, 144, 240
Carat 3, 25
Cassini - - - - 44, 49, 54
Cattle standard - - - - 3
Centesima 43
Centigram - - - 146, 147, 148
Centiliter ----- 144
Centime - - - - - 45
Centimeter 139
Centner 86
Centuria 43
C.G.S. or centimeter-gram-second-
system - - 102, 199, 205, 206
C.G.S. electro-magnetic units - 207
Chambers of Agriculture favour
metric svstem - - - 102
Chaney, H. J. - - 30, 37, 247
Chappuis, M. - - - - 261
Charlemagne 37
Charlemagne, " Pile de " - - 39
Chase, Salmon P. 126
Chicago congress - 208
Chisholm, H. W. - - 25, 32, 33, 244
Clark cell 207
Clark, Capt. A. R. - - - 69
Clarke's spheroid- 62
Coast and Geodetic Survey stand-
ards - - - 114, 121, 122
Colles, Geo. W. - - - - 133
Collet, M. A. - - - - 258
Cologne, Mark of - - 32, 40
Colonial Governors, British, favour
metric system - - - 159
Commemorative medal for metric
system - - - - 63, 64
Commercial pound (libra mercatoria) 33
Committee on coinage, weights
and measures reports 73, 75, 87,
90, 91, 120, 121, 128, 130, 133
Committee of weights and measures
and of moneys of Paris Ex-
position of 1867 - - - 85
Comparison of standards of length 229
Comparator of Borda - - - 230
Comparator of Lenoir - - - 230
Compensated bars - - - 251
Conder, C. R. - - - - 22
Condorcet - - - - 47, 48
Conference of British Colonial
Premiers - - - - 159
Congius 28
Congress, U.S., considers weights
and measures - - 113, 127
Congress, Acts of
119, 127, 128, 131, 132
Conservatoire des Arts et Metiers
69, 250, 251, 252
Conservatory, Meter of - - 73
INDEX
297
Continental Congress, legislation
on weights and measures, - 109
Corinth, Units of weight in - - 27
Corn bushel 35
Corn gallon 35
Corps Legislatif receives standard
meter and kilogram - - 63
Cotton values quoted decimally - 167
Coulomb 54
Coulomb, unit of quantity 203, 206, 207
Cross- wires - - - - 231, 234
Crypt chapel 30
Crystal standards - - - 236
Cubit - - 6, 13, 14, 15, 20, 22, 26
Cunin-Gridaine 83
Currency, Decimal - - 85, 110
Curvature, Unit of 202
Dagobert 37
Daniell cell 205
Deben or uten 24
De Bonnay, Marquis 46
Decagrams - 146, 148
Decaliter - 144, 145
Decameter - 138, 139
Decigrams - - - - 146, 148
Deciliter 144
Deciina 43
Decimal Association - - - 101
Decimal clocks ... - 168
Decimal hour .... 168
Decimal multiplication - - 167
Decimal system of coinage - 85,110
Decimal system of Jefferson - 111
Decimal system of money pro-
posed in France 45
Decimes 45
Decimeter - - - - 138, 139
Decistere - - - - - 144
Decuria 43
Didrachms 25
Delambre .... 54, 60
Delambre and Mechain, Base du
Systeme MUrique - - - 41
De Luc 99
Denier 38
Denmark signs metric treaty - 76
De Puvy, Charles A. - - - 168
De Sarzec, E. - - - 14
De Schubert, Gen. T. F. - - 69
Dessert-spoonful ... - 198
Digit 6
Directive force .... 202
Dividing engine - 225
Domesday book - - - 31
Double weighing - 237
Drachmas 27
Draughting room, Metric system
in 181
)rusus, Foot of -
PAGE
- 26
)unkirk
49, 56
)u Vernois, Prieur
- 44
Sarth inductor
- 204
3dgar, Laws of -
- 30
3d ward L, Laws of
- 34
fid ward II. . Laws of -
- 36, 242
Mward III., Laws of -
- 243
Sgypt, metric measures
- 92
Egyptian measures, Ancient
11, 20, 22, 23, 24
Ehalkus 27
Electrical congress, Chicago 208, 216
Electrical congress, Paris - - 215
Electrical congress (St. Louis) 216, 241
Electrical measure, U.S. units of 131
Electromotive force - - - 204
Elephantis, Cubit of - 22
Elizabeth, Standards of 34, 36, 243
Ell 26, 36, 89
Elle 83
End standard (metre a bouts) - 74
End standards (e talon a bouts) - 223
Energy, Unit of - - - - 202
Engineering, Metric system in - 172
England, Progress of metric
system in - - - - 98
English Bible, Weights and meas-
ures in 20
English parliamentary accounts
and papers 91
English yard
3, 31, 36, 243, 244, 245, 246
Ephah 20
Eratosthenes 29
Erg 202, 206
Euboic talent 27
Everest, Col. George 69
Exchequer, Standards of - 34, 109
Exodus, Weights and measures at
time of 20
Export business and uniform
measures .... 133
Ezekiel .... 20, 23
Fabbroni 256
Farad 203, 206
Farmers' Associations favour
metric system - - - 102
Fathom 6
Federal constitution, Weights and
measures in - - - - 109
Finland, metric system adopted - 95
Fizeau 261
Fleetwood, Bishop - - - 30
Floreal 53
Foerster, W. .... 87
Foot 6, 25, 26, 31, 37, 38, 44, 89, 112
298
INDEX
PAGE
Force, Units of - 200, 202
Forney, M. N. - - - - 185
Foster, Secretary of State - - 159
France, Measures of - - 37, 43
French Academy 99
French foot 38
French standards of length - 37, 249
French standards presented to
various nations - - - 83
French standards of weight 38, 250
Fructidor 53
Fundamental units - - S, 200
Fuss 83
42, 55
- 164
- 43
- 200
8, 89, 90
9, 22, 24
- 15
Galileo 15
Gallatin, Albert, Minister - 119,121
Gambey, Comparator of - 69, 232
Gan 15
Gar 15
Garden 15
Gas thermometer - - - 228
Gauges - - - 176, 177, 178
Gauss, Carl Friedrich - - 200, 201
Gauss (unit) .... 215
Genesis .... 11-19
Geodetic or trigonometrical survey
" Geometrical " inch -
Geometric foot
German Magnetic Union
Germany, Metric system in
86, 87,
Ghizeh, Pyramid of
Gin
Gird 30
Godin and Bouguer 44
Goldsmith's Hall, Standard of - 248
Gore, J. H. 43
Gouon and Penin 64
Gradus 26
Graham, George 36
Gram 54, 146
Gratings, Diffraction - - - 226
Gravimetric method - - - 193
Great circle 42, 48
Great rnina 16
Great pyramid - - 7, 9, 22, 24
Greaves, John - - - 29, 30
Greece, Measures of ancient - 25
Greece, Metric system in - - 92
Greek cubit - - - - 22, 25
Greek foot ----- 25
Gregorian calendar resumed in
France 53
Griffiths, F. L. - - - - 23
Gros 39, 66
Gudea scale - - - - 13, 14
Gunter, Edmund- 9S
Gur 16
Guillaume, Ch. Ed.
vii., 35, 39, 221, 223, 228
Guizot 83
Halsey and Dale, The Metric
Fallacy 134
Hamy, M. 261
Hand-breadth - - - - 6, 13
Harpham, F. E. - - - 41
Harris ------ 34
Harrison, President Benjamin - 131
Hassler - - 114, 121, 122, 123
Hastings, Charles S. - - - 211
Haute-Guyenne 45
Haiiy 54, 62
Hebrew weights and measures
19, 20, 21
Hectar(e) - - - - 51, 142
Hectogram - 51, 148
Hectoliter - - - - 51, 145
Hectometer - - - - 51, 139
Hekatompedos 25
Hekt 23
Henry (unit) - - - - 210
Henry L, Yard of - - - 3, 31
Henry III., Statutes. of - 32,
Henry IV.
Henry VII. 34,
Henry VIII., Statutes of -
Henry, Prof. Joseph -
Henu
Herschel, Sir John - - 7,
Hilgard, J. E. -
Hin
Hindus, Weights and measures of
Hiuen-Tsiang -
Holland, Metric system in - 82, 93,
Hoi ton, Michigan, Base at - - 141
Homer 21
Hommel - - - - 11, 12, 13
House of Commons Committee
report - - - -
House of Deputies, France, bill
Hultsch ....
Hundredweight -
Hungary, Metric system in -
Hunt, Wm. H. - - -
Huygens -
Hydrogen scale -
Hydrogen thermometer
33
33
35
34
129
23
164
129
21
18
6
94
100
67
25
156
91
195
43
228
228
Ibanez, General 77
Iced bar base apparatus - - 141
Ideler, L. 12
Imperial bushel - - - 35, 249
Imperial standards
245, 246, 247, 248, 249
Inch 26, 36
India, Ancient measures of - - 6
INDEX
299
PAGE
- 208
120, 121
186
181
200
216
208
216
75
209
Inductance, Unit of
Ingham, S. D. -
Institution of Electrical Engineers
Instruments of precision, Use of
metric system in -
Intensity of magnetism, Measure-
ment of
International American Conference
of 1890 - 103, 159
International ampere - - - 209
International Bureau of Weights
and Measures - 75, 76, 77, 129,
221, 226, 260
International Commission
61, 72, 9
International Congress of Elec-
tricians (Chicago) -
International Congress of Elec-
tricians (Paris) - - 207, 208
International Congress of Elec-
tricians (St. Louis)
International Convention of
Weights and Measures
International Coulomb
International electrical units
131, 199, 209
International farad - - - 209
International Geodetic Association 71
International kilogram, Definition
of - - - - ." . " 78
International metric commission
72, 73, 74, 75, 76, 77, 78
International metric prototype
standards - 76, 77, 252, 254, 255,
256, 257, 258, 259
International ohm - - 207-209
International Postal Convention 127
International Postal Union - - 151
International prototype meter
130, 136, 221, 252, 255
International standard kilogram
78, 258, 259
International Statistical Congress 126
International volt - - - 209
Invariability of standards - 219, 260
Israelites, measures - - 19, 20, 21
Italy, Metric system in - - 93
Jacobi 205
Japanese weights and measures - 93
Jefferson, Thomas
110, 111, 112, 113, 114, 115
Jeremiah 23
Jews, Weights and measures of - 19
Johns, Rev. C. H. U. - - 16, 17, 18
Josephus 10
Jomard - - - - 10, 30
Joule ---- 206, 208, 209
Jugerum 26
Ka
Kab -
Karsten
Kasbu -
Kat or Kiti -
Kater, Captain Henry
99, 100, 119, 120,
Keith, Rev. George Skene
Kelly -
Kelvin -
Kennedy, A. R. S.
Khar - - -
Khet --- -
Kilogauss
Kilogram 50, 62, 63, 73,
147, 256,
Kilogram of the Archives
73, 74, 75, 147,
Kilometer -
Kilowatt
King Edgar -
Kirwan
Kiti or Kat -
Koenigsberg standard -
Kohlrausch, Rudolf
Kor ....
Korn-Tonde-
Kupffer
PAGE
- 16
16, 21
- 40
- 15
- 24
122, 222, 245
- 99
31, 37
- 101
- 20
- 23
- 23
- 215
74-146,
257, 258, 259
256, 257, 258
- 50, 138
- 206
- 30
- 98
- 24
- 223
- 201, 205
- 21
- 96
- 234
47:
Lacaille
La Condamine
Lagrange
Lalande
Laplace - -47, 48,
Larsam or Larsa -
Lathes -
Latin prefixes
Latin Union
Latitude, Determination of
56, 57, 58, 59
Lavoisier .... 62, 98, 99
Leading screw of lathes - - 187
■ 49
- 44
48, 54
- 229
54, 65, 98, 99
- 13
- 182
- 137
- 85
Lefevre-Gineau
Lehmann
Lenoir -
Lepsius
Leroux, Alfred
Lever comparator
Le Verrier -
Libbrae metrica -
Libra -
Libra mercatoria
Library catalogue cards
Lieue -
Lignes -
Line and reel
Line standards (etalon a
Linnard, J. H.
Liter ....
62, 256
15, 18
14, 230, 251, 256
13, 22
- 71
- 230
- 69
- 82
- 28
- 33
- 140
- 97
44, 45
- 23
- 223
- 134
54, 145
traits)
300
INDEX
PAGE
Liverpool Cotton Association - 167
Livre 39, 45, 97
Livre de Troyes - 33
Livre Esterlin ... 32, 38
Livre poid de marc 39
London Exposition of 1851 - 83, 84
Longitude 59
Long ton 168
Louis XVI. 45
Lumber, Measurement of - - 178
Maass concordats - - 83, 97
Machine shop, Metric system in - 182
Madison, President James - - 115
Magna Charta, Weights and
measures in - - - - 32
Magnetic field, Unit of - - 203
Magnetic pole, Unit of - - 202
Maine approves metric system - 122
Mairan, Toise of - - - 61
Marc 39
Marc de Troyes - - - - 33
Marine Hospital Service - 192-195
Mark of Cologne 32, 40
Mass, Measures of 146
Master Car Builders' Association
173, 185
Mauss, C. 250
Maxwell, (unit) - - - 203, 215
Maxwell, J. Clark - - - 260
Measures of capacity - - 144, 240
Mechain - - - 41, 54, 60, 61
Mechanical engineering and manu-
facturing, Metric system in - 172
Mechanical engineers, American
Society of - 145-162
Medical department of the army
192, 195, 196
Medical department of the navy
192, 195
Medical papyri 24
Medicine and pharmacy, Metric
system in 191
Medimnus 23
Megameter 138
Memphis, Necropolis at - - 22
Memphis-Faium road - - - 23
Mendenhall, J. C. - - - 164
Mesures usuelles - - 65, 66, 67
Meter - - 49-54, 62-63, 139
Meter of the Archives 62, 71, 73, 75,
221, 225, 249, 251
Meter of the conservatory - 63, 251
Meter of the observatory - - 251
Method of interference for measur-
ing differences of length - 225
Metre a bouts 74
Metre a traits - - - 72, 73, 74
Metric measures of capacity 144, 240
PAGE
Metric measures of length - - 138
Metric measures of mass - - 146
Metric measures of surface - - 142
Metric measures of volume - - 143
Metric prescriptions - - - 192
Metric standard of U.S. Coast
Survey 114
Metric standard of United States 130
Metric system - - 39, 41, 61, 63
Metric system in U.S. Congress
133, 134
Metric thread .... 183
Metric ton 147
Metric wire gauges - - - 178
Metrological Society, American - 129
Mexico, Metric system in - - 103
Michelson, Prof. A.
211, 260, 261, 262, 263, 264, 265
Micro-farad 206
Micrometer-microscope
230, 231, 233, 234
Micrometer screws - - - 229
Micron 140
Milan, Metric system introduced
in 82
Mile 26, 31
Milia pasuum - - - 26, 31
Miller, W. H. - - - 35, 248
Miller, Sir John Riggs - 99, 163
Milligram - - . 146, 148
Milligram weights - - - 148
Milliliter 144
Millimeter - 138; 140
Millimicron - 138^ 140
Mina - - -16,21,25,27,28,32
Mina, Babylonian 16
Mina, heavy - - - - 16
Mina, light 16
Mina, Phoenician 16
Mint, U.S., standard troy pound 119
M'Leod 99
Modius 28
Moment of rotation, Unit of - 202
Momentum, Unit of - 202
Monge 48, 54, 99
Moore, Dr. 123
Morin, General A. - - 41, 69
Morris, Robert - - - - 110
Mouton, Gabriel - - - - 43
Miinzpfund - - - • - - 86
Myriameter 138
Myriagram - • - - 146, 147
Napoleon I. - - - 65, 77, 82, 92
Napoleon III. - - - - 71
National Academy of France - 49
National Academy of Sciences,
U.S. - - - 127,129,211
National Assembly (French) - 46
INDEX
301
PAOE
National Bureau of Standards - 132
National Institute of Sciences and
Arts (French) - - 53, 63
National Physical Laboratory
(England) - - - 152, 241
National prototype meter of the
United States - - - 130
Natural standards 5
Natural units - - - - 5
Neutral plane .... 222
New Hampshire approves metric
system 125
Newton's rings - 261
New Zealand adopts metric system 102
Nickel five cent, piece- - - 128
Noak, Ark of - - - - 11
Normal-Aichungs-Kommission 87, 90
North German Confederation - 87
Norway - - - - 95, 96
Oboles -
.
38, 39
Ohm - - ,-
.
- 206
Ohm's law -
.
- 204, 206
Oke -
.
- - 92
Oldberg, Oscar
-
- 195
Old Testament, Weights and
measures of - - - 19, 20, 21
Olympian foot 25
Oner 21
Opticians' use of metric system - 181
Orguia, or fathom - - - 25
Origin of weights and measures - 1 i
Ounce - - - - 25, 26, 32, 33
Pace 2, 6
Palestine Exploration Fund,
Quarterly statement, 1902 - 22
Palm - 6
Palm, Babylonian - - - 14
Palmipes or foot 26
Parasang - - - - - 15
Paris Academy of Sciences 46, 47, 71
Paris Exposition - - 70, 84, 85, 129
Paris International Electrical
Congress - - 207, 208, 215
Parliamentary reports 91
Parliament, Burning of Houses of,
1834 35
Parliamentary standard - - 249
Parthenon 25
Par value 167
Passus ------ 26
Paucton - - - - 7, 10, 37
Pavilion Breteuil - - - 77
Pence 32
Pendulum as a unit of length
15, 37, 42, 44, 46, 48, 49, 111, 245
Penny, or sterling - - - 32
Pennyweight - - - - 32
Perch ... -
PAGE
- 45
Perche -
- 97
Perpignan, Base at
- 55
Pertica or Decempeda -
- 26
Peru, Toise de
44, 249
Petrie, Flinders -
- 18, 23, 24
Pfund -
- 82, 83, 86
Philippine Tariff Act, 1901 - - 132
Philosophical drachm, ounce, and
pound 98
Phoenician weights and measures 18, 21
Physicalisch Technische Reich san-
stalt 152
Picard 43
Pied de roi 37
Pied geometrique 44
Pied (Swiss) .... 97
Pile of Charlemagne - - 39, 250
Pinte (French) - 145
Platinum for standards - 236, 257
Platinum Iridium standards
74, 77, 148, 221, 252
Platinum metres • - - 62, 251
Pliny 26
Plumb-line 15
Plutarch 25
Pluviose 53
Polar axis ----- 164
Polar flattening - - - 48, 59, 62
Polaris 39
Polar radius - - - - 164
Polybius 26
Polychrome Bible - - - 14
Porto Rico, Metric measures in - 132
Portugal, Metric system in - - 94
Postal Congress of 1863 - - 126
Pot (Swiss) 97
Potential difference, Unit of - 203
Pound - 27, 32, 33, 34, 38. 119, 248
Power, Unit of - - - - 202
Pratt & Whitney Co. - - - 185
Prairial 53
Prescriptions, Metric - - - 197
Priestley, Dr. - - - - 98
Prony 54
Ptolemy Lagos 24
Pyx chapel 30
Quadrant (unit of inductance) - 208
Quantity of electricity, Unit 203, 209
Quarteron ----- 39
Quarteron (Swiss unit of capacity) 97
Queen Anne, Gallon of - - 35
Queen Elizabeth, Standards of
35, 36, 243, 247
Quintal ... - 146, 147
Quito, arc 44
Railway shares
167
302
INDEX
Rawlinson -
Rayleigh, Lord •
Rayon astronomique
Reed -
Regnault
Reichsanstalt
Resistance -
Retail Trades Associations favour
metric system
Rhine countries, Measures in
Rhine foot -
Richard L, Laws of - -
Riders
Ridge way 3
PAGE
- 13
- 207
- 43
- 15
- 69
152, 241
203, 204, 205
102
26
40
31
148
4, 18
Rock crystal standards 148, 236
Rogers, Wm. A. - - - 185, 235
Rome, Weights and measures of - 26
Rosenberger - - - 204, 205
Rosebery, Lord - 101
Rowland, Henry A. - 207, 211, 226
Royal foot (French) ... 37
Royal Society (British)
46, 47, 84, 99, 101
Ruggles, Samuel B. - - - 126
Ruprecht balance - - - 237
Russia, Weights and measures of 94
Ruthe 82
Salces, Base at - - -
Sagene
Sar
Sauvage, Ed.
Saxon weights and measures 30,
Schoenus ....
31
55
94
15
183
,32
23
Schools, Metric system in 125, 129, 165
Schiraz, Anania de
Schumacher, Professor
Screws, Cutting of
Screw-cutting lathe
Screw threads 182, 183, 184, 185
Seah -
Second's pendulum
15, 36, 37
48, 49,
44
25
248
182
186
186
21
46,
Sellers, Dr. Coleman
Sellers, Wm.
Seller's standard -
Seller's thread
Senkereh tablet -
Sensibility of balance -
Sexagesimal system
Sextarii
Shaku -
Shaw-Caldecott, W. -
She - - - -
Sheet and plate iron and
U.S. standard scale
Shekel, Babylonian
Shekels of the Hebrews
Shilling - -
111, 245
- 161
- 183
- 183
- 185
13, 17
- 239
- 12
- 28
- 93
13, 17
- 15
steel,
131
16
21
32
PAGE
Shoppen 83
Short ton 168
Shuckburgh, Sir George
120, 230, 231, 245
Shuckburgh scale - - - 100
Shuckburgh's comparator - 230, 231
Siemens, Alex. - - 186, 216, 217
Siemens, Werner - 205
Silver coinage by metric weight - 128
Silver voltameter - 210,211,212
Sizes of screw threads -
Skaal-Pund
Smith, Prof. R. H.
Smyth, Piazzi -
Societe d'Eneouragement pour
l'lndustrie Nationale
Solid angle unit -
Solive
Solon - - - -
Sols
Solvay Process Company
South America, Metric system
used in
South and Central America, Metric
system employed in 103, 107
Spain, Adoption of metric system
in
Span
Spanish Geographical and Statis-
tical Institute
Spartan States use Babylonian
talent -
Specific gravity of standard
184
96
135
10
183
- 202
- 65
- 27
38, 39
- 168
Specific gravity tables
160
108
95
6
158
27
- 238
290, 291
Specifications for ampere and volt 211
Spencer - - - - - 102
Square measures - 142
Stadion 25
Standard avoirdupois pound - 248
Standard bars for base measure-
ments -
Standard kilogram and meter
Standard cell 212, 213, 214
Standard gauges -
Standardization -
Standards of capacity -
Standard sizes
Standard troy pound of 1758
Standard troy pound, U.S. Mint
Standard yard (Elizabeth) -
Standard yard (Henry VII.)
Standard yard, British
244, 245, 246, 247
Standard yards of United States 114, 247
Standards and comparison - - 218
Standards Commission, British 35, 100
Standards office -
Standards of mass
Standards of the Netherlands
215
141
254
216
176
154
240
175
34
119
36, 243
36, 243
246
236
93
INDEX
303
PAGE
Standards of the United States - 122
Standards of resistance - - 241
Standards of resistance, current
and electrical pressure - - 242
Standards, Permanence of - - 228
State standards - - - 121, 122
Steel tape 140
Stere 54, 144
Sternberg, Gen. Geo. M. - - 196
Strabo 23, 26
St. Louis Exposition - - - 216
St. Petersburg Academy of
Sciences 71
Sweden, Metric system adopted - 95
Switzerland, Metric system in 82, 97
Syrian standard 21
Systeme International, S.I. or
S.J. 183
Table-spoonful - - - - 198
Talent, Alexandrian - - - 25
Talleyrand 46
Taps and dies .... 183
Teachers' Associations endorse
metric system - - - 102
Teaspoonful 198
Tel-el-Amarna correspondence - 19
Temperature measurements - - 227
Thermidor 53
Thermometers, thermometric meas-
urements ... . 227
Thermometer scales, Table of - 290
Tillet 47
Tittman, 0. H. - - - - 120
Toise 38, 44, 97
Toise de macons 38
Toise de Perou - - 38, 54, 249
Toise du Grand Chatelet - 38, 249
Torque, Unit of - - - - 202
Tortuosity, Unit of - - - 202
Totten, C. A. S. - - - - 10
Tours, Standards of - - 39
Tower Pound - - - 32, 33, 34
Tralles- - - - 62, 81, 82, 114
Transits 58
Treasury Department, U.S., Stan-
dards of - 123
Treaty, Metric 75
Tresca - - 74, 252, 253, 254, 255
Trigonometrical survey - - 55
Troughton 230
Troughton scale - 114, 121, 122, 247
Troy pound - - 25, 33, 34, 119, 248
Troyes, Standards of - - 33, 39
Trowbridge, John - - - 211
Tumblerful 198
Tungri, Belgic foot of - - - 31
Turkey, Measures of - - - 97
Tweedmouth - - - - 102 I
PAGE
Ulna - - - - - - 26
Ulna or Aulne - - - - 31
Unit acceleration - - - 200'
United States, Weights and meas-
ures of - - - - 103, 109
United States Army, Med. Dept. 195
United States Bureau of Standards 131
United States Navy, Med. Dept. 195
United States Pharmacopoeia - 192
Unit of Intensity of Magnetism - 200
Units 1
Unit velocity - - - - 200
Units, Absolute - - - - 200
Units, Arbitrary 5
Units, Fundamental 8
Units, Natural ... - 5
Upton, J. K. - - - - 91
Ush 15
Usuelle - - - - 65, 66, 67
Vauclain, S. M. -
Vandermonde
Van Swinden
Vendemiaire
Vernet, Base near
Vienna coin treaty
Virga or Verge -
Virga - - - -
Virgula geometrica
Volt - - -
Volume, Measures of -
Von Humboldt, Alex. -
- 188
- 54
- 61, 80, 82,
- 53
- 55
- 85
- 31
- 43
- 43
206, 209, 212
- 143
- 200
Wales, Philip S. - - - - 195
Warren, Gen. Charles 10
Washburne, E. B. - - - 130
Washington, President - 111, 113
Watchmakers use of metric threads 181
Water clock 12
Watt (unit) - - 202, 206, 208, 209
Watt, James 98
Wave length of light - 229,260,261,
262, 263, 264, 265, 266
Weber, Wilhelm - - 201,204,205
Weighing, Earliest - - - 4
Weights and Measures Act
(British, 1878) - - - 101
Westminster Abbey - - - 30
Weston cell 216
Wheat bushels - - - - 156
Whitworth standard - - 183, 186
Willans & Robinson, Messrs. - 187
William the Conqueror, Decree of 30
Williams, R. P. - - - - 125
Winchester standards - - - 30
Winchester bushel - - 35, 122
Winchester corn gallon - - 35
Wine gallon - - - - 35
304
INDEX
PAGE
Wine glass - - - - - 198
Windom, Secretary of the Treasury 159
Wire and sheet metals
Wolf, C. -
Wolf, M. -
Wolff, F. A.
Wollaston, Wm. H.
Wood worth, John M.
Work, Unit of -
176
62, 230, 251
- 230
- 206, 215
- 99
- 195
202, 206
World's Columbian Exposition - 208
Wrottesley, Sir John
PAGE
99
Yard or gird 30, 31
Yard standards - 36, 1 14, 243, 247
Yates, James 84
Young, Dr. Thomas 99
Yusdrumin pound of Charlemagne 29
Zollpfund
Zollverein
86, 89
- 86
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